title: Kim Coates

text: At the 7th Canadian Screen Awards, Coates won the award for Best Actor in a Continuing Leading Dramatic Role for his performance as gangster Declan Gardiner in the television series "Bad Blood".


title: Kim Coates

text: Coates supports the One Heart Source, a non profit organization aiming at ending poverty by designing high quality global initiatives focused on education and health.


title: Kim Coates

text: Coates lives in Los Angeles, California with his wife, Diana Chappell, and two children, Kyla and Brenna. He is known to be good friends with Prison Break co-star William Fichtner, as well as Kevin Costner and "Sons of Anarchy" co-star Theo Rossi. Coates became a United States citizen in 2010.


title: Ariana Richards

text: Ariana Clarice Richards is an American painter and former actress. She is best known for her role as Lex Murphy in the blockbuster film "Jurassic Park". Richards won several Young Artist Awards for her acting as a child, but as an adult has focused primarily on her art career.


title: Ariana Richards

text: Richards was born in Healdsburg, California, the daughter of Darielle (née Garrison), a public relations representative and film producer, and Gary Richards. Her sister, Bethany, is also an actress. Her maternal grandmother, who was of Italian ancestry, was a descendant of Renaissance painter Carlo Crivelli. In addition to Italian, her maternal grandfather, William Otto Garrison's father, John, had English ancestry. Richards is a descendant of boxer John L. Sullivan, who had Irish ancestry.


title: Ariana Richards

text: Richards married Mark Aaron Bolton in Oregon in January 2013; Bolton is an Irish immigrant, stunt performer, and a former soldier of the Irish Defence Forces. The couple have a daughter (born 2015).


title: Ariana Richards

text: Richards made her acting debut in 1987's "Into the Homeland", a made-for-cable release that starred Powers Boothe. She also appeared as Mindy Sterngood in the first "Tremors" film and reprised her role in the second sequel "", which went straight-to-video.


title: Ariana Richards

text: Her most notable appearance was as Lex Murphy in the first "Jurassic Park" film; she reprised the role briefly in the sequel "". She has been featured in other films such as "Angus", where she played a high school cheerleader; she also appeared on television episodes of "The Golden Girls", "Empty Nest" and "Boy Meets World".


title: Ariana Richards

text: In addition to acting in movies, Richards appeared in the 1997 music video "Brick" by Ben Folds Five, portraying a high school student having an abortion. She appeared in the September 2006 issue of the British movie magazine "Empire" discussing a possible return to acting. Richards starred in the 2013 film Battledogs, shot in Buffalo, New York.


title: Ariana Richards

text: On December 17, 1993, Richards released a CD album "First Love" on the Pony Canyon label in Japan. The album was released only in Japan and is rare and out-of-print. The tracks from the CD can be viewed on the YouTube channel of Philip Jennelle. The album was a mix between teen-pop and dance-friendly ballads of the early 1990s. There was also a single released in very small volume. Ariana and her mother wrote the words to the track "You're The Reason".


title: Ariana Richards

text: 15 years later, Richards returned briefly to the world of music in September 2008 and released a cover version of David Foster's "The Prayer" in a duet with Chris M. Allport, whom she has known since a young age.


title: Ariana Richards

text: Richards has become a successful artist. Her paintings, usually of landscapes and figures, tend to be in the style of the impressionists. In October 2005, she won first place in the National Professional Oil Painting Competition (sponsored by "American Artist" magazine) for the painting "Lady of the Dahlias".


title: Ajax the Great

text: Ajax () or Aias (; , "Aíantos"; archaic ) is a Greek mythological hero, the son of King Telamon and Periboea, and the half-brother of Teucer. He plays an important role, and is portrayed as a towering figure and a warrior of great courage in Homer's "Iliad" and in the Epic Cycle, a series of epic poems about the Trojan War, being second only to Achilles among Greek heroes of the war. He is also referred to as "Telamonian Ajax" (, in Etruscan recorded as "Aivas Tlamunus"), "Greater Ajax", or "Ajax the Great", which distinguishes him from Ajax, son of Oileus, also known as Ajax the Lesser.


title: Ajax the Great

text: Ajax is the son of Telamon, who was the son of Aeacus and grandson of Zeus, and his first wife Periboea. Through his uncle Peleus (Telamon's brother), he is the cousin of Achilles, and is the elder half-brother of Teucer.


title: Ajax the Great

text: The etymology of his given name is uncertain. By folk etymology his name was said to come from the root of "aiazō" "to lament", translating to "one who laments; mourner". Hesiod provided a different folk etymology in a story in his "The Great Eoiae", where Ajax receives his name when Heracles prays to Zeus that a son might be born to Telemon and Eriboea: Zeus sends an eagle ("aetos" αετός) as a sign, and Heracles then bids the parents call their son Ajax after the eagle.


title: Ajax the Great

text: Many illustrious Athenians, including Cimon, Miltiades, Alcibiades and the historian Thucydides, traced their descent from Ajax. On an Etruscan tomb dedicated to Racvi Satlnei in Bologna (5th century BC) there is an inscription that says "aivastelmunsl", which means "[family] of Telamonian Ajax".


title: Ajax the Great

text: In the account of Dares the Phrygian, Ajax was illustrated as ". . .powerful. His voice was clear, his hair black and curly. He was perfectly single-minded and unrelenting in the onslaught of battle." Meanwhile, In Homer's "Iliad" he is described as of great stature, colossal frame, and strongest of all the Achaeans. Known as the "bulwark of the Achaeans", he was trained by the centaur Chiron (who had trained Ajax's father Telamon and Achilles' father Peleus and later died of an accidental wound inflicted by Heracles, whom he was at the time training) at the same time as Achilles. He was described as fearless, strong, and powerful but also with a very high level of combat intelligence. Ajax commands his army wielding a huge shield made of seven cowhides with a layer of bronze. Most notably, Ajax is not wounded in any of the battles described in the "Iliad", and he is the only principal character on either side who does not receive substantial assistance from any of the gods (except for Agamemnon) who take part in the battles, although, in book 13, Poseidon strikes Ajax with his staff, renewing his strength. Unlike Diomedes, Agamemnon, and Achilles, Ajax appears as a mainly defensive warrior, instrumental in the defense of the Greek camp and ships and that of Patroclus' body. When the Trojans are on the offensive, he is often seen covering the retreat of the Achaeans. Significantly, while one of the deadliest heroes in the whole poem, Ajax has no aristeia depicting him on the offensive.


title: Ajax the Great

text: In the "Iliad", Ajax is notable for his abundant strength and courage, seen particularly in two fights with Hector. In Book 7, Ajax is chosen by lot to meet Hector in a duel which lasts most of a whole day. Ajax at first gets the better of the encounter, wounding Hector with his spear and knocking him down with a large stone, but Hector battles on until the heralds, acting at the direction of Zeus, call a draw, with the two combatants exchanging gifts, Ajax giving Hector a purple sash and Hector giving Ajax his sharp sword.


title: Ajax the Great

text: The second fight between Ajax and Hector occurs when the latter breaks into the Mycenaean camp, and battles with the Greeks among the ships. In Book 14, Ajax throws a giant rock at Hector which almost kills him. In Book 15, Hector is restored to his strength by Apollo and returns to attack the ships. Ajax, wielding an enormous spear as a weapon and leaping from ship to ship, holds off the Trojan armies virtually single-handedly. In Book 16, Hector and Ajax duel once again. Hector then disarms Ajax (although Ajax is not hurt) and Ajax is forced to retreat, seeing that Zeus is clearly favoring Hector. Hector and the Trojans succeed in burning one Greek ship, the culmination of an assault that almost finishes the war. Ajax is responsible for the death of many Trojan lords, including Phorcys.


title: Ajax the Great

text: Ajax often fought in tandem with his brother Teucer, known for his skill with the bow. Ajax would wield his magnificent shield, as Teucer stood behind picking off enemy Trojans.


title: Ajax the Great

text: Achilles was absent during these encounters because of his feud with Agamemnon. In Book 9, Agamemnon and the other Mycenaean chiefs send Ajax, Odysseus and Phoenix to the tent of Achilles in an attempt to reconcile with the great warrior and induce him to return to the fight. Although Ajax speaks earnestly and is well received, he does not succeed in convincing Achilles.


title: Ajax the Great

text: When Patroclus is killed, Hector tries to steal his body. Ajax, assisted by Menelaus, succeeds in fighting off the Trojans and taking the body back with his chariot; however, the Trojans have already stripped Patroclus of Achilles' armor. Ajax's prayer to Zeus to remove the fog that has descended on the battle to allow them to fight or die in the light of day has become proverbial. According to Hyginus, in total, Ajax killed 28 people at Troy.


title: Ajax the Great

text: As the "Iliad" comes to a close, Ajax and the majority of other Greek warriors are alive and well. When Achilles dies, killed by Paris (with help from Apollo), Ajax and Odysseus are the heroes who fight against the Trojans to get the body and bury it with his companion, Patroclus. Ajax, with his great shield and spear, manages to recover the body and carry it to the ships, while Odysseus fights off the Trojans. After the burial, each claims Achilles' magical armor, which had been forged on Mount Olympus by the smith-god Hephaestus, for himself as recognition for his heroic efforts. A competition is held to determine who deserves the armor. Ajax argues that because of his strength and the fighting he has done for the Greeks, including saving the ships from Hector, and driving him off with a massive rock, he deserves the armor. However, Odysseus proves to be more eloquent, and with the aid of Athena, the council gives him the armor. Ajax, distraught by this result and "conquered by his own grief", plunges his sword into his own chest, killing himself. In the Little Iliad, Ajax goes mad with rage at Odysseus' victory and slaughters the cattle of the Greeks. After returning to his senses, he kills himself out of shame.


title: Ajax the Great

text: The Belvedere Torso, a marble torso now in the Vatican Museums, is considered to depict Ajax "in the act of contemplating his suicide".


title: Ajax the Great

text: In Sophocles' play "Ajax", a famous retelling of Ajax's demise, after the armor is awarded to Odysseus, Ajax feels so insulted that he wants to kill Agamemnon and Menelaus. Athena intervenes and clouds his mind and vision, and he goes to a flock of sheep and slaughters them, imagining they are the Achaean leaders, including Odysseus and Agamemnon. When he comes to his senses, covered in blood, he realizes that what he has done has diminished his honor, and decides that he prefers to kill himself rather than live in shame. He does so with the same sword which Hector gave him when they exchanged presents. From his blood sprang a red flower, as at the death of Hyacinthus, which bore on its leaves the initial letters of his name "Ai", also expressive of lament. His ashes were deposited in a golden urn on the Rhoetean promontory at the entrance of the Hellespont.


title: Ajax the Great

text: Ajax's half-brother Teucer stood trial before his father for not bringing Ajax's body or famous weapons back. Teucer was acquitted for responsibility but found guilty of negligence. He was disowned by his father and was not allowed to return to his home, the island of Salamis off the coast of Athens.


title: Ajax the Great

text: Homer is somewhat vague about the precise manner of Ajax's death but does ascribe it to his loss in the dispute over Achilles' armor; when Odysseus visits Hades, he begs the soul of Ajax to speak to him, but Ajax, still resentful over the old quarrel, refuses and descends silently back into Erebus.


title: Ajax the Great

text: Like Achilles, he is represented (although not by Homer) as living after his death on the island of Leuke at the mouth of the Danube. Ajax, who in the post-Homeric legend is described as the grandson of Aeacus and the great-grandson of Zeus, was the tutelary hero of the island of Salamis, where he had a temple and an image, and where a festival called "Aianteia" was celebrated in his honour. At this festival a couch was set up, on which the panoply of the hero was placed, a practice which recalls the Roman Lectisternium. The identification of Ajax with the family of Aeacus was chiefly a matter which concerned the Athenians, after Salamis had come into their possession, on which occasion Solon is said to have inserted a line in the "Iliad" (2.557–558), for the purpose of supporting the Athenian claim to the island. Ajax then became an Attic hero; he was worshipped at Athens, where he had a statue in the market-place, and the tribe "Aiantis" was named after him. Pausanias also relates that a gigantic skeleton, its kneecap in diameter, appeared on the beach near Sigeion, on the Trojan coast; these bones were identified as those of Ajax.


title: Ajax the Great

text: In 2001, Yannos Lolos began excavating a Mycenaean palace near the village of Kanakia on the island of Salamis which he theorized to be the home of the mythological Aiacid dynasty. The multi-story structure covers and had perhaps 30 rooms. The palace appears to have been abandoned at the height of the Mycenaean civilization, roughly the same time the Trojan War may have occurred.


title: Dirty John (TV series)

text: Dirty John is an American true crime anthology television series, based on the podcast of the same name by Christopher Goffard, that premiered on November 25, 2018, on Bravo. Outside the United States, it was made available through Netflix on February 14, 2019. The series was created by Alexandra Cunningham also an executive producer alongside Richard Suckle, Charles Roven, Mark Herzog, Christopher G. Cowen, and Chris Argentieri. The series was initially given an order for two seasons. In May 2019, it was announced that the series will be moving from Bravo to USA Network, ahead of the premiere of the second season. The second season is titled "Dirty John: The Betty Broderick Story". A trailer for the season was released on March 25, 2020, featuring Christian Slater and Amanda Peet in the role of Betty Broderick. In April 2020, it was announced that the second season would premiere on June 2, 2020, with a sneak peek of the first episode of the second season airing on May 31, 2020.


title: Dirty John (TV series)

text: The first season was met with a mixed to positive response from critics upon its premiere and managed to garner recognition at various award ceremonies. Connie Britton earned nominations for awards including the Golden Globe Award for Best Actress – Miniseries or Television Film and the Critics' Choice Television Award for Best Actress in a Limited Series or Movie Made for Television and Garner earned a nomination for the Critics' Choice Television Award for Best Supporting Actress in a Limited Series or Movie Made for Television.


title: Dirty John (TV series)

text: Season one of "Dirty John" tells the story of "how a romance with the charismatic John Meehan spiraled into secrets, denial, manipulation, and ultimately, survival – with horrific consequences for an entire family."


title: Dirty John (TV series)

text: Season two follows the breakdown of Betty Broderick’s marriage to childhood sweetheart Dan Broderick and the devastating effects of the emotional toll it took on Betty.


title: Dirty John (TV series)

text: On January 28, 2018, it was announced that Bravo had given a series order to "Dirty John", a new television series created and written by Alexandra Cunningham. The series order was reportedly for two seasons in which Cunningham would executive produce alongside Richard Suckle, Charles Roven, Mark Herzog, Christopher G. Cowen and Christopher Argentieri. Production companies involved in the series were slated to include Universal Cable Productions, Los Angeles Times Studios, and Atlas Entertainment. On October 8, 2018, it was announced that the series would premiere on November 25, 2018. On May 17, 2019, it was reported that the series will be moving from Bravo to USA Network, ahead of the premiere of the second season. On September 9, 2019, it was reported that series is an anthology series and the second season is titled "Dirty John: The Betty Broderick Story" which premiered on June 2, 2020.


title: Dirty John (TV series)

text: On March 26, 2018, it was announced that Connie Britton had been cast in the series' lead role. On April 3, 2018, it was reported that Eric Bana had joined the main cast as the eponymous John Meehan. On June 14, 2018, it was announced that Jean Smart had been cast in a recurring role. In July 2018, it was reported that Juno Temple, Julia Garner, Kevin Zegers, Keiko Agena, John Karna, Sprague Grayden, Cliff Chamberlain, Jake Abel, and David Barrera had joined the cast. Temple and Garner were cast in starring roles and Zegers, Abel, and Barrera were set to appear in a recurring capacity. On August 16, 2018, it was announced that Lindsey Kraft had been cast in a guest starring role. On September 9, 2019, Amanda Peet and Christian Slater were cast in starring roles for the second season. On October 18, 2019, Missi Pyle and Holley Fain were cast in recurring roles for the second season. On November 8, 2019, Rachel Keller joined the main cast while Emily Bergl, Lena Georgas, Tiera Skovbye, and Chris Mason joined the cast in recurring capacities.


title: Dirty John (TV series)

text: On August 24, 2018, a "first look" still image from the series was released featuring Connie Britton and Eric Bana as Debra Newell and John Meehan. On September 17, 2018, a teaser trailer for the series was released. On October 8, 2018, the official trailer for the series was released. On December 20, 2018, an exclusive preview clip from the series was released.


title: Dirty John (TV series)

text: On November 13, 2018, the series held its official premiere at NeueHouse Hollywood in Los Angeles, California featuring a screening of the series. A red carpet arrival was originally scheduled to take place before the screening but it was canceled out of respect for the victims of the Woolsey Fire which was still burning in the Los Angeles and Ventura counties. The first season became available to stream on Netflix worldwide on February 14, 2019 and later added to Netflix in the US in November 2019. "Dirty John" premiered in the United Kingdom on April 10, 2021 on 5Star.


title: Dirty John (TV series)

text: On January 28, 2018, it was announced that Oxygen had ordered a companion docuseries to air alongside the main series which would investigate the real John Meehan through the eyes of those he deceived. The project was set to be executive produced by Mark Herzog and Christopher G. Cowen with production companies including Herzog & Co and Los Angeles Times Studios. On November 14, 2018, it was reported that the docuseries was actually a documentary, that it had been titled "Dirty John: The Dirty Truth", and that it would air in January 2019. On December 16, 2018, it was announced that documentary would premiere on January 14, 2019.


title: Dirty John (TV series)

text: The series has been met with a mixed to positive response from critics upon its premiere. On the review aggregation website Rotten Tomatoes, the first season holds a 71% approval rating with an average rating of 5.51/10 based on 34 reviews. The website's critical consensus reads, ""Dirty John" might not live up to the thrills of its source material, but Connie Britton puts on a clinic with her interpretation of true crime treachery." Metacritic, which uses a weighted average, assigned the first season a score of 58 out of 100 based on 18 critics, indicating "mixed or average reviews".


title: Dirty John (TV series)

text: In a positive review, "Entertainment Weekly"s Kristen Baldwin gave the first season a grade of "A−" and directed particular praise at the performances in it describing Britton as "perfectly cast" and saying of Bana that he "may benefit the most from "Dirty John"; as Meehan, the actor pivots from charming to chilling and back again with astonishing ease." In a similarly favorable analysis, the "Los Angeles Times"s Mike Mack commended the first season declaring, "Glossy and well-acted, its transfer from your daily commute's most suspenseful listening stretch ever to serviceable wine-and-laundry-folding companion show feels, all in all, a smooth one."


title: Dirty John (TV series)

text: In a more mixed assessment, "RogerEbert.com"s Brian Tallerico gave the first season qualified praise saying, ""Dirty John" is very entertaining, though it's not without faults. It doesn't dig very deep, or present Debra's daughters as full characters (their main roles are to look confused or upset, which is a waste of big talent), and its storytelling can be a little convoluted. But it never claims to be high art." In an outright negative appraisal, "TVLine"s Dave Nemetz gave the first season a grade of "D" and criticized it saying, "Britton and her talented co-stars are wasted here on a warmed-over Lifetime movie masquerading as a prestige TV miniseries — one that's, sadly, not even trashy enough to qualify as a guilty pleasure." In another unfavorable evaluation, "IndieWire"s Ben Travers was very critical of the series' first season giving it a grade of "C−" and saying that, "Decidedly not ambitious 'prestige' television, the first three episodes make perfectly clear this isn't a nuanced series, or one interested in exploring abuse or manipulation in serious fashion. It's trying to be a juicy nighttime soap that uses the 'true story' tag to drive viewers' mouths further and further agape."


title: Dirty John (TV series)

text: Review aggregator Rotten Tomatoes reported an approval rating of 90% based on 20 reviews, with an average rating of 7.15/10 for the second season. The website's critics consensus states, "Although "The Betty Broderick Story" sensational story is at times scattershot, Amanda Peet's incredible embodiment of a woman scorned is a sight to behold." Metacritic gave the second season a score of 73 out of 100 based on 12 critics, indicating "generally favorable reviews".


title: Technocracy

text: Technocracy is a form of government in which the decision-maker or makers are selected based on their expertise in a given area of responsibility, particularly with regard to scientific or technical knowledge. This system explicitly contrasts with representative democracy, the notion that elected representatives should be the primary decision-makers in government, though it does not necessarily imply eliminating elected representatives. Decision-makers are selected based on specialized knowledge and performance rather than political affiliations, parliamentary skills, or popularity.


title: Technocracy

text: The term "technocracy" was initially used to signify the application of the scientific method to solving social problems. In its most extreme form, technocracy is an entire government running as a technical or engineering problem and is mostly hypothetical. In more practical use, technocracy is any portion of a bureaucracy run by technologists. A government in which elected officials appoint experts and professionals to administer individual government functions, and recommend legislation, can be considered technocratic. Some uses of the word refer to a form of meritocracy, where the ablest are in charge, ostensibly without the influence of special interest groups. Critics have suggested that a "technocratic divide" challenges more participatory models of democracy, describing these divides as "efficacy gaps that persist between governing bodies employing technocratic principles and members of the general public aiming to contribute to government decision making".


title: Technocracy

text: The term "technocracy" is derived from the Greek words τέχνη, "tekhne" meaning "skill" and κράτος, "kratos" meaning "power", as in "governance", or "rule". William Henry Smyth, a California engineer, is usually credited with inventing the word "technocracy" in 1919 to describe "the rule of the people made effective through the agency of their servants, the scientists and engineers", although the word had been used before on several occasions. Smyth used the term "Technocracy" in his 1919 article "'Technocracy'—Ways and Means to Gain Industrial Democracy" in the journal "Industrial Management" (57). Smyth's usage referred to Industrial democracy: a movement to integrate workers into decision-making through existing firms or revolution.


title: Technocracy

text: In the 1930s, through the influence of Howard Scott and the technocracy movement he founded, the term technocracy came to mean 'government by technical decision making', using an energy metric of value. Scott proposed that money be replaced by energy certificates denominated in units such as ergs or joules, equivalent in total amount to an appropriate national net energy budget, and then distributed equally among the North American population, according to resource availability.


title: Technocracy

text: There is in common usage found the derivative term "technocrat". The word "technocrat" can refer to someone exercising governmental authority because of their knowledge, "a member of a powerful technical elite", or "someone who advocates the supremacy of technical experts". McDonnell and Valbruzzi define a prime minister or minister as a technocrat if "at the time of their appointment to government, they: have never held public office under the banner of a political party; are not a formal member of any party; and are said to possess recognized non-party political expertise which is directly relevant to the role occupied in government". In Russia, the President of Russia has often nominated ministers based on technical expertise from outside political circles, and these have been referred to as "technocrats".


title: Technocracy

text: Before the term "technocracy" was coined, technocratic or quasi-technocratic ideas involving governance by technical experts were promoted by various individuals, most notably early socialist theorists such as Henri de Saint-Simon. This was expressed by the belief in state ownership over the economy, with the state's function being transformed from pure philosophical rule over men into a scientific administration of things and a direction of production processes under scientific management. According to Daniel Bell:


title: Technocracy

text: "St. Simon's vision of industrial society, a vision of pure technocracy, was a system of planning and rational order in which society would specify its needs and organize the factors of production to achieve them." Citing the ideas of St. Simon, Bell concludes that the "administration of things" by rational judgment is the hallmark of technocracy.


title: Technocracy

text: Alexander Bogdanov, a Russian scientist and social theorist, also anticipated a conception of technocratic process. Both Bogdanov's fiction and his political writings, which were highly influential, suggest that he expected a coming revolution against capitalism to lead to a technocratic society.


title: Technocracy

text: From 1913 until 1922, Bogdanov immersed himself in writing a lengthy philosophical treatise of original ideas, "Tectology: Universal Organization Science". Tectology anticipated many basic ideas of systems analysis, later explored by cybernetics. In "Tectology", Bogdanov proposed unifying all social, biological, and physical sciences by considering them as systems of relationships and seeking organizational principles that underlie all systems.


title: Technocracy

text: Arguably, the Platonic idea of philosopher-kings represents a sort of technocracy in which the state is run by those with specialist knowledge, in this case, knowledge of the Good rather than scientific knowledge. The Platonic claim is that those who best understand goodness should be empowered to lead the state, as they would lead it toward the path of happiness. Whilst knowledge of the Good differs from knowledge of science, rulers are here appointed based on a certain grasp of technical skill rather than democratic mandate.


title: Technocracy

text: Technocrats are individuals with technical training and occupations who perceive many important societal problems as being solvable with the applied use of technology and related applications. The administrative scientist Gunnar K. A. Njalsson theorizes that technocrats are primarily driven by their cognitive "problem-solution mindsets" and only in part by particular occupational group interests. Their activities and the increasing success of their ideas are thought to be a crucial factor behind the modern spread of technology and the largely ideological concept of the "information society". Technocrats may be distinguished from "econocrats" and "bureaucrats" whose problem-solution mindsets differ from those of the technocrats.


title: Technocracy

text: In 2013, a European Union library briefing on its legislative structure referred to the Commission as a "technocratic authority", holding a "legislative monopoly" over the EU lawmaking process. The briefing suggests that this system, which elevates the European Parliament to a vetoing and amending body, was "originally rooted in the mistrust of the political process in post-war Europe". This system is unusual since the Commission's sole right of legislative initiative is a power usually associated with Parliaments.


title: Technocracy

text: The former government of the Soviet Union has been referred to as a technocracy. Soviet leaders like Leonid Brezhnev often had a technical background. In 1986, 89% of Politburo members were engineers.


title: Technocracy

text: Leaders of the Chinese Communist Party used to be mostly professional engineers. According to surveys of municipal governments of cities with a population of 1 million or more in China, it has been found that over 80% of government personnel had a technical education. Under the five-year plans of the People's Republic of China, projects such as the National Trunk Highway System, the China high-speed rail system, and the Three Gorges Dam have been completed. During China's 20th National Congress, a class of technocrats in finance and economics are replaced in favor of high-tech technocrats.


title: Technocracy

text: Several governments in European parliamentary democracies have been labelled 'technocratic' based on the participation of unelected experts ('technocrats') in prominent positions. Since the 1990s, Italy has had several such governments (in Italian, "governo tecnico") in times of economic or political crisis, including the formation in which economist Mario Monti presided over a cabinet of unelected professionals. The term 'technocratic' has been applied to governments where a cabinet of elected professional politicians is led by an unelected prime minister, such as in the cases of the 2011-2012 Greek government led by economist Lucas Papademos and the Czech Republic's 2009–2010 caretaker government presided over by the state's chief statistician, Jan Fischer. In December 2013, in the framework of the national dialogue facilitated by the Tunisian National Dialogue Quartet, political parties in Tunisia agreed to install a technocratic government led by Mehdi Jomaa.


title: Technocracy

text: The article "Technocrats: Minds Like Machines" states that Singapore is perhaps the best advertisement for technocracy: the political and expert components of the governing system there seem to have merged completely. This was underlined in a 1993 article in "Wired" by Sandy Sandfort, where he describes the information technology system of the island even at that early date making it effectively intelligent.


title: Technocracy

text: Following Samuel Haber, Donald Stabile argues that engineers were faced with a conflict between physical efficiency and cost efficiency in the new corporate capitalist enterprises of the late nineteenth-century United States. Because of their perceptions of market demand, the profit-conscious, non-technical managers of firms where the engineers work often impose limits on the projects that engineers desire to undertake.


title: Technocracy

text: The prices of all inputs vary with market forces, thereby upsetting the engineer's careful calculations. As a result, the engineer loses control over projects and must continually revise plans. To maintain control over projects, the engineer must attempt to control these outside variables and transform them into constant factors.


title: Technocracy

text: The American economist and sociologist Thorstein Veblen was an early advocate of technocracy and was involved in the Technical Alliance, as were Howard Scott and M. King Hubbert (the latter of whom later developed the theory of peak oil). Veblen believed technological developments would eventually lead to a socialistic reorganization of economic affairs. Veblen saw socialism as one intermediate phase in an ongoing evolutionary process in society that would be brought about by the natural decay of the business enterprise system and the rise of the engineers. Daniel Bell sees an affinity between Veblen and the Technocracy movement.


title: Technocracy

text: In 1932, Howard Scott and Marion King Hubbert founded Technocracy Incorporated and proposed that money be replaced by energy certificates. The group argued that apolitical, rational engineers should be vested with the authority to guide an economy into a thermodynamically balanced load of production and consumption, thereby doing away with unemployment and debt.


title: Technocracy

text: The technocracy movement was briefly popular in the US in the early 1930s during the Great Depression. By the mid-1930s, interest in the movement was declining. Some historians have attributed the decline to the rise of Roosevelt's New Deal.


title: Technocracy

text: Historian William E. Akin rejects this conclusion. Instead, Akin argues that the movement declined in the mid-1930s due to the technocrats' failure to devise a 'viable political theory for achieving change'. Akin postulates that many technocrats remained vocal, dissatisfied, and often sympathetic to anti-New Deal third-party efforts.


title: Technocracy

text: Critics have suggested that a "technocratic divide" exists between a governing body controlled to varying extents by technocrats and members of the general public. Technocratic divides are "efficacy gaps that persist between governing bodies employing technocratic principles and members of the general public aiming to contribute to government decision making". Technocracy privileges the opinions and viewpoints of technical experts, exalting them into a kind of aristocracy while marginalizing the opinions and viewpoints of the general public.


title: Technocracy

text: As major multinational technology corporations (e.g., FAANG) swell market caps and customer counts, critiques of technocratic government in the 21st century see its manifestation in American politics not as an "authoritarian nightmare of oppression and violence" but rather as an éminence grise: a democratic cabal directed by Mark Zuckerberg and the entire cohort of "Big Tech" executives. It is not explained how Mark Zuckerberg or other big tech corporate heads (who are not elected by the people) can form a "democratic" cabal. In his 1982 Technology and Culture journal article, "The Technocratic Image and the Theory of Technocracy", John G. Gunnell presciently writes: "...politics is increasingly subject to the influence of technological change", with specific reference to the advent of The Long Boom and the genesis of the Internet, following the 1973-1975 Recession. Gunnel goes on to add three levels of analysis that delineate technology's political influence:


title: Technocracy

text: In each of the three analytical levels, Gunnell foretells technology's infiltration of political processes and suggests that the entanglement of the two (i.e. technology and politics) will inevitably produce power concentrations around those with advanced technological training, namely the technocrats. Forty years after the publication of Gunnell's writings, technology and government have become, for better or for worse, increasingly intertwined. Facebook can be considered a technocratic microcosm, a "technocratic nation-state" with a cyberspatial population that surpasses any terrestrial nation. In a broader sense, critics fear that the rise of social media networks (e.g. Twitter, YouTube, Instagram, Pinterest), coupled with the "decline in mainstream engagement", imperil the ""networked young citizen"" to inconspicuous coercion and indoctrination by algorithmic mechanisms, and, less insidiously, to the persuasion of particular candidates based predominantly on "Social Media engagement".


title: Technocracy

text: In a 2022 article published in "Boston Review", political scientist Matthew Cole highlights two problems with technocracy: that it creates "unjust concentrations of power" and relies on a "flawed theory of knowledge." With respect to the first point, Cole argues that technocracy excludes citizens from policy-making processes while advantaging elites. With respect to the second, he argues that the value of expertise is overestimated in technocratic systems, and points to an alternative concept of "smart democracy" which enlists the knowledge of ordinary citizens.


title: Valknut

text: The valknut is a symbol consisting of three interlocked triangles. It appears on a variety of objects from the archaeological record of the ancient Germanic peoples. The term "valknut" is a modern development; it is not known what term or terms were used to refer to the symbol historically.


title: Valknut

text: Scholars have proposed a variety of explanations for the symbol, sometimes associating it with the god Odin, and it has been compared to the three-horned symbol found on the 9th-century Snoldelev Stone, to which it may be related.


title: Valknut

text: The valknut appears on a wide variety of objects found in areas inhabited by the Germanic peoples. The symbol is prominently featured on the Nene River Ring, an Anglo-Saxon gold finger ring dated to around the 8th to 9th centuries. A wooden bed in the Viking Age Oseberg Ship buried near Tønsberg, Norway features a carving of the symbol on an ornately stylized bedpost and the Oseberg tapestry fragments, a partially preserved tapestry found within the ship burial, also features the symbol. Additionally, the valknut appears prominently on two picture stones from Gotland, Sweden: the Stora Hammars I stone and the Tängelgårda stone.


title: Valknut

text: The historically attested instances of the symbol appear in two traditional, topologically distinct, forms. The symbol appears in unicursal form, topologically a trefoil knot also seen in the triquetra. This unicursal form is found, for example, on the Tängelgårda stone. The symbol also appears in tricursal form, consisting of three linked triangles, topologically equivalent to the Borromean rings. This tricursal form can be seen on one of the Stora Hammars stones, as well as upon the Nene River Ring, and on the Oseberg ship bed post. Although other forms are topologically possible, these are the only attested forms found so far.


title: Valknut

text: In Norwegian Bokmål, the term "valknute" is used for a polygon with a loop on each of its corners. In the English language the looped four-cornered symbol is called Saint John's Arms.


title: Valknut

text: Chapter 17 of the 13th century "Prose Edda" book "Skáldskaparmál" contains the following description of the heart of the jötunn Hrungnir; "Hrungnir had a heart that was famous. It was made of hard stone with three sharp-pointed corners just like the carved symbol "hrungnishjarta" [Hrungnir's heart]." Comparisons have been made between this symbol description and the symbol known as the valknut.


title: Valknut

text: For instance, beside the figure of Odin on his horse shown on several memorial stones there is a kind of knot depicted, called the "valknut", related to the triskele. This is thought to symbolize the power of the god to bind and unbind, mentioned in the poems and elsewhere. Odin had the power to lay bonds upon the mind, so that men became helpless in battle, and he could also loosen the tensions of fear and strain by his gifts of battle-madness, intoxication, and inspiration.


title: Valknut

text: Davidson says that similar symbols are found beside figures of wolves and ravens on "certain cremation urns" from Anglo-Saxon cemeteries in East Anglia.


title: Valknut

text: Because the symbol appears on picture stones with Odin and on burial gifts in the Oseberg ship burial, Rudolf Simek says that the symbol may have been associated with religious practices surrounding death.


title: Valknut

text: The valknut is topologically equivalent to either the Borromean rings, the trefoil knot, or (in modern use only) a closed three-link chain, depending on the particular artistic depiction:


title: Valknut

text: The symbol is used for a variety of purposes in modern popular culture. The valknut symbol is used as a religious symbol by adherents of Heathenry, a new religious movement inspired by historic Germanic paganism.


title: Valknut

text: In Europe, the Swedish forest products company Svenska Cellulosa Aktiebolaget uses a triquetra valknut as their logo, which can be commonly seen on many products produced by the company; the DFB has used a logo inspired by the unicursal form of the valknut for the Germany national football team since 1991.


title: Valknut

text: The symbol appears as the fretboard inlay on some of Arch Enemy/Carcass guitarist Michael Amott's signature Dean Guitars "Tyrant" models, and it is also used as a logo by American engineering firm RedViking. In Civilization VI, the valknut is the national symbol of Norway, which in the game is led by Harald Hardrada and mostly representative of Vikings rather than the modern country.


title: Valknut

text: The valknut has seen some use by White supremacists. The Anti-Defamation League notes that "nonracist pagans may also use this symbol, so one should carefully examine it in context rather than assume that a particular use of the symbol is racist."


title: Scenes from a Marriage (American miniseries)

text: Scenes from a Marriage is an American drama television miniseries developed, written and directed by Hagai Levi produced for HBO and starring Oscar Isaac and Jessica Chastain. It is an English-language remake of the 1973 Swedish miniseries of the same name by Ingmar Bergman. It was presented at the 2021 Venice Film Festival and it premiered on September 12, 2021 on HBO.


text: It was announced in July 2020 that HBO had given the miniseries a greenlight, with Hagai Levi writing and directing and Oscar Isaac and Michelle Williams serving as executive producers. Upon the miniseries order announcement, Isaac and Williams were also cast to star. Williams would be forced to exit her starring role in October due to a scheduling conflict, but would remain as an executive producer. She was replaced with Jessica Chastain. In November 2020, Sunita Mani was cast in a supporting role. Nicole Beharie, Corey Stoll and Tovah Feldshuh would join in supporting roles in January 2021.


text: Filming began in New York City in October 2020, and was halted for two weeks in November after two production staff members tested positive for COVID-19.


text: The five-episode limited series had its world premiere at the 78th Venice International Film Festival in the out of competition category. The limited series premiered on September 12, 2021 on HBO.


text: The review aggregator website Rotten Tomatoes reported a 81% approval rating with an average rating of 7.50/10, based on 48 critic reviews. The website's critics consensus reads, "Though "Scenes from a Marriage"s straightforward approach at times struggles to justify its existence, Jessica Chastain and Oscar Isaac's crackling chemistry and impressive performances are a sight to behold." Metacritic gave the series a weighted average score of 70 out of 100 based on 24 critic reviews, indicating "generally favorable reviews".


title: Permutation

text: In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.


title: Permutation

text: Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory.


title: Permutation

text: Permutations are used in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences.


title: Permutation

text: The number of permutations of distinct objects is  factorial, usually written as , which means the product of all positive integers less than or equal to .


title: Permutation

text: Technically, a permutation of a set is defined as a bijection from to itself. That is, it is a function from to for which every element occurs exactly once as an image value. This is related to the rearrangement of the elements of in which each element is replaced by the corresponding . For example, the permutation (3, 1, 2) mentioned above is described by the function formula_1 defined as


title: Permutation

text: The collection of all permutations of a set form a group called the symmetric group of the set. The group operation is the composition (performing two given rearrangements in succession), which results in another rearrangement. As properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set formula_3 that are considered for studying permutations.


title: Permutation

text: In elementary combinatorics, the -permutations, or partial permutations, are the ordered arrangements of distinct elements selected from a set. When is equal to the size of the set, these are the permutations of the set.


title: Permutation

text: Permutations called hexagrams were used in China in the I Ching (Pinyin: Yi Jing) as early as 1000 BC.


title: Permutation

text: Al-Khalil (717–786), an Arab mathematician and cryptographer, wrote the "Book of Cryptographic Messages". It contains the first use of permutations and combinations, to list all possible Arabic words with and without vowels.


title: Permutation

text: The rule to determine the number of permutations of "n" objects was known in Indian culture around 1150 AD. The "Lilavati" by the Indian mathematician Bhaskara II contains a passage that translates to:


title: Permutation

text: The product of multiplication of the arithmetical series beginning and increasing by unity and continued to the number of places, will be the variations of number with specific figures.


title: Permutation

text: In 1677, Fabian Stedman described factorials when explaining the number of permutations of bells in change ringing. Starting from two bells: "first, "two" must be admitted to be varied in two ways", which he illustrates by showing 1 2 and 2 1. He then explains that with three bells there are "three times two figures to be produced out of three" which again is illustrated. His explanation involves "cast away 3, and 1.2 will remain; cast away 2, and 1.3 will remain; cast away 1, and 2.3 will remain". He then moves on to four bells and repeats the casting away argument showing that there will be four different sets of three. Effectively, this is a recursive process. He continues with five bells using the "casting away" method and tabulates the resulting 120 combinations. At this point he gives up and remarks:


title: Permutation

text: Now the nature of these methods is such, that the changes on one number comprehends the changes on all lesser numbers, ... insomuch that a compleat Peal of changes on one number seemeth to be formed by uniting of the compleat Peals on all lesser numbers into one entire body;


title: Permutation

text: Stedman widens the consideration of permutations; he goes on to consider the number of permutations of the letters of the alphabet and of horses from a stable of 20.


title: Permutation

text: A first case in which seemingly unrelated mathematical questions were studied with the help of permutations occurred around 1770, when Joseph Louis Lagrange, in the study of polynomial equations, observed that properties of the permutations of the roots of an equation are related to the possibilities to solve it. This line of work ultimately resulted, through the work of Évariste Galois, in Galois theory, which gives a complete description of what is possible and impossible with respect to solving polynomial equations (in one unknown) by radicals. In modern mathematics, there are many similar situations in which understanding a problem requires studying certain permutations related to it.


title: Permutation

text: The simplest example of permutations is permutations without repetitions where we consider the number of possible ways of arranging items into places. The factorial has special application in defining the number of permutations in a set which does not include repetitions. The number n!, read "n factorial", is precisely the number of ways we can rearrange n things into a new order. For example, if we have three fruits: an orange, apple and pear, we can eat them in the order mentioned, or we can change them (for example, an apple, a pear then an orange). The exact number of permutations is then formula_4. The number gets extremely large as the number of items (n) goes up.


title: Permutation

text: In a similar manner, the number of arrangements of k items from n objects is sometimes called a partial permutation or a k-permutation. It can be written as formula_5 (which reads "n permute k"), and is equal to the number formula_6 (also written as


title: Permutation

text: In mathematics texts it is customary to denote permutations using lowercase Greek letters. Commonly, either formula_1 and formula_8, or formula_9 and formula_10 are used.


title: Permutation

text: Permutations can be defined as bijections from a set onto itself. All permutations of a set with "n" elements form a symmetric group, denoted formula_11, where the group operation is function composition. Thus for two permutations, formula_10 and formula_13 in the group formula_11, the four group axioms hold:


title: Permutation

text: As a bijection from a set to itself, a permutation is a function that "performs" a rearrangement of a set, and is not an arrangement itself. An older and more elementary viewpoint is that permutations are the arrangements themselves. To distinguish between these two, the identifiers "active" and "passive" are sometimes prefixed to the term "permutation", whereas in older terminology "substitutions" and "permutations" are used.


title: Permutation

text: A permutation can be decomposed into one or more disjoint "cycles", that is, the orbits, which are found by repeatedly tracing the application of the permutation on some elements. For example, the permutation formula_13 defined by formula_31 has a 1-cycle, formula_32 while the permutation formula_10 defined by formula_34 and formula_35 has a 2-cycle formula_36 (for details on the syntax, see below). In general, a cycle of length "k", that is, consisting of "k" elements, is called a "k"-cycle.


title: Permutation

text: An element in a 1-cycle formula_37 is called a fixed point of the permutation. A permutation with no fixed points is called a derangement. 2-cycles are called transpositions; such permutations merely exchange two elements, leaving the others fixed.


title: Permutation

text: Since writing permutations elementwise, that is, as piecewise functions, is cumbersome, several notations have been invented to represent them more compactly. "Cycle notation" is a popular choice for many mathematicians due to its compactness and the fact that it makes a permutation's structure transparent. It is the notation used in this article unless otherwise specified, but other notations are still widely used, especially in application areas.


title: Permutation

text: In Cauchy's "two-line notation", one lists the elements of "S" in the first row, and for each one its image below it in the second row. For instance, a particular permutation of the set "S" = {1, 2, 3, 4, 5} can be written as


title: Permutation

text: this means that "σ" satisfies , , , , and . The elements of "S" may appear in any order in the first row. This permutation could also be written as:


title: Permutation

text: If there is a "natural" order for the elements of "S", say formula_41, then one uses this for the first row of the two-line notation:


title: Permutation

text: Under this assumption, one may omit the first row and write the permutation in "one-line notation" as


title: Permutation

text: that is, as an ordered arrangement of the elements of "S". Care must be taken to distinguish one-line notation from the cycle notation described below. In mathematics literature, a common usage is to omit parentheses for one-line notation, while using them for cycle notation. The one-line notation is also called the "word representation" of a permutation. The example above would then be since the natural order would be assumed for the first row. (It is typical to use commas to separate these entries only if some have two or more digits.) This form is more compact, and is common in elementary combinatorics and computer science. It is especially useful in applications where the elements of "S" or the permutations are to be compared as larger or smaller.


title: Permutation

text: Cycle notation describes the effect of repeatedly applying the permutation on the elements of the set. It expresses the permutation as a product of cycles; since distinct cycles are disjoint, this is referred to as "decomposition into disjoint cycles".


title: Permutation

text: In addition, each cycle can be written in different ways, by choosing different starting points; for example,


title: Permutation

text: One may combine these equalities to write the disjoint cycles of a given permutation in many different ways.


title: Permutation

text: 1-cycles are often omitted from the cycle notation, provided that the context is clear; for any element "x" in "S" not appearing in any cycle, one implicitly assumes formula_53. The identity permutation, which consists only of 1-cycles, can be denoted by a single 1-cycle (x), by the number 1, or by "id".


title: Permutation

text: A convenient feature of cycle notation is that cycle notation of the inverse permutation is given by reversing the order of the elements in the permutation's cycles. For example,


title: Permutation

text: In some combinatorial contexts it is useful to fix a certain order for the elements in the cycles and of the (disjoint) cycles themselves. Miklós Bóna calls the following ordering choices the "canonical cycle notation":


title: Permutation

text: For example, (312)(54)(8)(976) is a permutation in canonical cycle notation. The canonical cycle notation does not omit one-cycles.


title: Permutation

text: Richard P. Stanley calls the same choice of representation the "standard representation" of a permutation, and Martin Aigner uses the term "standard form" for the same notion. Sergey Kitaev also uses the "standard form" terminology, but reverses both choices; that is, each cycle lists its least element first and the cycles are sorted in decreasing order of their least, that is, first elements.


title: Permutation

text: There are two ways to denote the composition of two permutations. formula_55 is the function that maps any element "x" of the set to formula_56. The rightmost permutation is applied to the argument first,


title: Permutation

text: Since function composition is associative, so is the composition operation on permutations: formula_57. Therefore, products of more than two permutations are usually written without adding parentheses to express grouping; they are also usually written without a dot or other sign to indicate composition.


title: Permutation

text: but to that end permutations must be written to the "right" of their argument, often as an exponent, where "σ" acting on "x" is written "x"; then the product is defined by . However this gives a "different" rule for multiplying permutations; this article uses the definition where the rightmost permutation is applied first.


title: Permutation

text: The concept of a permutation as an ordered arrangement admits several generalizations that are not permutations, but have been called permutations in the literature.


title: Permutation

text: A weaker meaning of the term "permutation", sometimes used in elementary combinatorics texts, designates those ordered arrangements in which no element occurs more than once, but without the requirement of using all the elements from a given set. These are not permutations except in special cases, but are natural generalizations of the ordered arrangement concept. Indeed, this use often involves considering arrangements of a fixed length "k" of elements taken from a given set of size "n", in other words, these k"-permutations of "n are the different ordered arrangements of a "k"-element subset of an "n"-set (sometimes called variations or arrangements in older literature). These objects are also known as partial permutations or as sequences without repetition, terms that avoid confusion with the other, more common, meaning of "permutation". The number of such formula_58-permutations of formula_59 is denoted variously by such symbols as formula_60, formula_61, formula_62, formula_63, or formula_64, and its value is given by the product


title: Permutation

text: The product is well defined without the assumption that formula_59 is a non-negative integer, and is of importance outside combinatorics as well; it is known as the Pochhammer symbol formula_68 or as the formula_58-th falling factorial power formula_70 of formula_59.


title: Permutation

text: This usage of the term "permutation" is closely related to the term "combination". A "k"-element combination of an "n"-set "S" is a "k" element subset of "S", the elements of which are not ordered. By taking all the "k" element subsets of "S" and ordering each of them in all possible ways, we obtain all the "k"-permutations of "S". The number of "k"-combinations of an "n"-set, "C"("n","k"), is therefore related to the number of "k"-permutations of "n" by:


title: Permutation

text: Ordered arrangements of "k" elements of a set "S", where repetition is allowed, are called "k"-tuples. They have sometimes been referred to as permutations with repetition, although they are not permutations in general. They are also called words over the alphabet "S" in some contexts. If the set "S" has "n" elements, the number of "k"-tuples over "S" is formula_74


title: Permutation

text: There is no restriction on how often an element can appear in an "k"-tuple, but if restrictions are placed on how often an element can appear, this formula is no longer valid.


title: Permutation

text: If "M" is a finite multiset, then a multiset permutation is an ordered arrangement of elements of "M" in which each element appears a number of times equal exactly to its multiplicity in "M". An anagram of a word having some repeated letters is an example of a multiset permutation. If the multiplicities of the elements of "M" (taken in some order) are formula_75, formula_76, ..., formula_77 and their sum (that is, the size of "M") is "n", then the number of multiset permutations of "M" is given by the multinomial coefficient,


title: Permutation

text: A "k"-permutation of a multiset "M" is a sequence of length "k" of elements of "M" in which each element appears "a number of times less than or equal to" its multiplicity in "M" (an element's "repetition number").


title: Permutation

text: Permutations, when considered as arrangements, are sometimes referred to as "linearly ordered" arrangements. In these arrangements there is a first element, a second element, and so on. If, however, the objects are arranged in a circular manner this distinguished ordering no longer exists, that is, there is no "first element" in the arrangement, any element can be considered as the start of the arrangement. The arrangements of objects in a circular manner are called circular permutations. These can be formally defined as equivalence classes of ordinary permutations of the objects, for the equivalence relation generated by moving the final element of the linear arrangement to its front.


title: Permutation

text: Two circular permutations are equivalent if one can be rotated into the other (that is, cycled without changing the relative positions of the elements). The following four circular permutations on four letters are considered to be the same.


title: Permutation

text: The circular arrangements are to be read counter-clockwise, so the following two are not equivalent since no rotation can bring one to the other.


title: Permutation

text: The number of -permutations with disjoint cycles is the signless Stirling number of the first kind, denoted by .


title: Permutation

text: The cycles (including the fixed points) of a permutation formula_13 of a set with elements partition that set; so the lengths of these cycles form an integer partition of , which is called the cycle type (or sometimes cycle structure or cycle shape) of formula_13. There is a "1" in the cycle type for every fixed point of formula_13, a "2" for every transposition, and so on. The cycle type of formula_83 is formula_84


title: Permutation

text: More precisely, the general form is formula_85, where formula_86 are the numbers of cycles of respective length. The number of permutations of a given cycle type is


title: Permutation

text: In general, composing permutations written in cycle notation follows no easily described pattern – the cycles of the composition can be different from those being composed. However the cycle type is preserved in the special case of conjugating a permutation formula_13 by another permutation formula_10, which means forming the product formula_90. Here, formula_90 is the "conjugate" of formula_13 by formula_10 and its cycle notation can be obtained by taking the cycle notation for formula_13 and applying formula_10 to all the entries in it. It follows that two permutations are conjugate exactly when they have the same cycle type.


title: Permutation

text: The order of a permutation formula_13 is the smallest positive integer "m" so that formula_97. It is the least common multiple of its cycles lengths. For example, the order of formula_98 is formula_99.


title: Permutation

text: Although many such expressions for a given permutation may exist, either they all contain an even number of transpositions or they all contain an odd number of transpositions. Thus all permutations can be classified as even or odd depending on this number.


title: Permutation

text: This result can be extended so as to assign a "sign", written formula_100, to each permutation. formula_101 if formula_13 is even and formula_103 if formula_13 is odd. Then for two permutations formula_13 and formula_10


title: Permutation

text: A "permutation matrix" is an "n" × "n" matrix that has exactly one entry 1 in each column and in each row, and all other entries are 0. There are several different conventions that one can use to assign a permutation matrix to a permutation of {1, 2, ..., "n"}. One natural approach is to associate to the permutation "σ" the matrix formula_109 whose ("i", "j") entry is 1 if "i" = "σ"("j") and is 0 otherwise. This convention has two attractive properties: first, the product of matrices and of permutations is in the same order, that is, formula_110 for all permutations "σ" and "π". Second, if formula_111 represents the standard formula_112 column vector (the vector with "i"th entry equal to 1 and all other entries equal to 0), then formula_113.


title: Permutation

text: For example, with this convention, the matrix associated to the permutation formula_114 is formula_115 and the matrix associated to the permutation formula_116 is formula_117. Then the composition of permutations is formula_118, and the corresponding matrix product is


title: Permutation

text: It is also common in the literature to find the inverse convention, where a permutation "σ" is associated to the matrix formula_120 whose ("i", "j") entry is 1 if "j" = "σ"("i") and is 0 otherwise. In this convention, permutation matrices multiply in the opposite order from permutations, that is, formula_121 for all permutations "σ" and "π". In this correspondence, permutation matrices act by permuting indices of standard formula_122 row vectors formula_123: one has formula_124.


title: Permutation

text: In some applications, the elements of the set being permuted will be compared with each other. This requires that the set "S" has a total order so that any two elements can be compared. The set {1, 2, ..., "n"} is totally ordered by the usual "≤" relation and so it is the most frequently used set in these applications, but in general, any totally ordered set will do. In these applications, the ordered arrangement view of a permutation is needed to talk about the "positions" in a permutation.


title: Permutation

text: An "ascent" of a permutation "σ" of "n" is any position "i" < "n" where the following value is bigger than the current one. That is, if "σ" = "σ""σ"..."σ", then "i" is an ascent if "σ" < "σ".


title: Permutation

text: Similarly, a "descent" is a position "i" < "n" with "σ" > "σ", so every "i" with formula_125 either is an ascent or is a descent of "σ".


title: Permutation

text: An "ascending run" of a permutation is a nonempty increasing contiguous subsequence of the permutation that cannot be extended at either end; it corresponds to a maximal sequence of successive ascents (the latter may be empty: between two successive descents there is still an ascending run of length 1). By contrast an "increasing subsequence" of a permutation is not necessarily contiguous: it is an increasing sequence of elements obtained from the permutation by omitting the values at some positions.


title: Permutation

text: For example, the permutation 2453167 has the ascending runs 245, 3, and 167, while it has an increasing subsequence 2367.


title: Permutation

text: The number of permutations of "n" with "k" ascents is (by definition) the Eulerian number formula_126; this is also the number of permutations of "n" with "k" descents. Some authors however define the Eulerian number formula_126 as the number of permutations with "k" ascending runs, which corresponds to descents.


title: Permutation

text: An excedance of a permutation "σ""σ"..."σ" is an index "j" such that . If the inequality is not strict (that is, ), then "j" is called a "weak excedance". The number of "n"-permutations with "k" excedances coincides with the number of "n"-permutations with "k" descents.


title: Permutation

text: There is a relationship between the one-line notation and the canonical cycle notation. Consider the permutation formula_128 in canonical cycle notation; if we simply remove the parentheses, we obtain the permutation formula_129 in one-line notation. Foata's transition lemma establishes the nature of this correspondence as a bijection on the set of "n"-permutations (to itself). Richard P. Stanley calls this correspondence the "fundamental bijection".


title: Permutation

text: Let formula_130 be the parentheses-erasing transformation which returns formula_131 in one-line notation when given formula_132 in canonical cycle notation. As stated, formula_133 operates by simply removing all parentheses. The operation of the inverse transformation, formula_134, which returns formula_132 in canonical cycle notation when given formula_131 in one-line notation, is a bit less intuitive. Given the one-line notation formula_137, the first cycle of formula_132 in canonical cycle notation must start with formula_139. As long as the subsequent elements are smaller than formula_139, we are in the same cycle of formula_132. The second cycle of formula_132 starts at the smallest index formula_143 such that formula_144. In other words, formula_145 is larger than everything else to its left, so it is called a "left-to-right maximum". Every cycle in the canonical cycle notation starts with a left-to-right maximum.


title: Permutation

text: For example, in the permutation formula_146, 5 is the first element larger than the starting element 3, so the first cycle of formula_132 must be formula_148. Then 8 is the next element larger than 5, so the second cycle is formula_149. Since 9 is larger than 8, formula_150 is a cycle by itself. Finally, 9 is larger than all the remaining elements to its right, so the last cycle is formula_151. Concatenating these 4 cycles gives formula_152 in canonical cycle notation.


title: Permutation

text: The following table shows both formula_131 and formula_132 for the six permutations of formula_155. The bold side of each equality shows the permutation using its designated notation (one-line notation for formula_131 and canonical cycle notation for formula_132) while the non-bold side shows the same permutation in the other notation. Comparing the bold side of each column of the table shows the parenthesis removing/restoring operation of Foata's bijection, while comparing the same side of each column (for example, the LHS) shows which permutations are mapped to themselves by the bijection (first 3 rows) and which are not (last 3 rows).


title: Permutation

text: As a first corollary, the number of n-permutations with exactly "k" left-to-right maxima is also equal to the signless Stirling number of the first kind, formula_158. Furthermore, Foata's mapping takes an "n"-permutation with "k"-weak excedances to an "n"-permutations with ascents. For example, (2)(31) = 321 has two weak excedances (at index 1 and 2), whereas has one ascent (at index 1; that is, from 2 to 3).


title: Permutation

text: An "inversion" of a permutation "σ" is a pair of positions where the entries of a permutation are in the opposite order: formula_159 and formula_160. So a descent is just an inversion at two adjacent positions. For example, the permutation has three inversions: (1, 3), (2, 3), and (4, 5), for the pairs of entries (2, 1), (3, 1), and (5, 4).


title: Permutation

text: Sometimes an inversion is defined as the pair of values whose order is reversed; this makes no difference for the "number" of inversions, and this pair (reversed) is also an inversion in the above sense for the inverse permutation "σ". The number of inversions is an important measure for the degree to which the entries of a permutation are out of order; it is the same for "σ" and for "σ". To bring a permutation with "k" inversions into order (that is, transform it into the identity permutation), by successively applying (right-multiplication by) adjacent transpositions, is always possible and requires a sequence of "k" such operations. Moreover, any reasonable choice for the adjacent transpositions will work: it suffices to choose at each step a transposition of "i" and where "i" is a descent of the permutation as modified so far (so that the transposition will remove this particular descent, although it might create other descents). This is so because applying such a transposition reduces the number of inversions by 1; as long as this number is not zero, the permutation is not the identity, so it has at least one descent. Bubble sort and insertion sort can be interpreted as particular instances of this procedure to put a sequence into order. Incidentally this procedure proves that any permutation "σ" can be written as a product of adjacent transpositions; for this one may simply reverse any sequence of such transpositions that transforms "σ" into the identity. In fact, by enumerating all sequences of adjacent transpositions that would transform "σ" into the identity, one obtains (after reversal) a "complete" list of all expressions of minimal length writing "σ" as a product of adjacent transpositions.


title: Permutation

text: The number of permutations of "n" with "k" inversions is expressed by a Mahonian number, it is the coefficient of "X" in the expansion of the product


title: Permutation

text: which is also known (with "q" substituted for "X") as the q-factorial <nowiki>[</nowiki>"n"<nowiki>]</nowiki>! . The expansion of the product appears in Necklace (combinatorics).


title: Permutation

text: where formula_168 denotes Bruhat order in the symmetric groups. This graded partial order often appears in the context of Coxeter groups.


title: Permutation

text: One way to represent permutations of "n" things is by an integer "N" with 0 ≤ "N" < "n"!, provided convenient methods are given to convert between the number and the representation of a permutation as an ordered arrangement (sequence). This gives the most compact representation of arbitrary permutations, and in computing is particularly attractive when "n" is small enough that "N" can be held in a machine word; for 32-bit words this means "n" ≤ 12, and for 64-bit words this means "n" ≤ 20. The conversion can be done via the intermediate form of a sequence of numbers "d", "d", ..., "d", "d", where "d" is a non-negative integer less than "i" (one may omit "d", as it is always 0, but its presence makes the subsequent conversion to a permutation easier to describe). The first step then is to simply express "N" in the "factorial number system", which is just a particular mixed radix representation, where, for numbers less than "n"!, the bases (place values or multiplication factors) for successive digits are , , ..., 2!, 1!. The second step interprets this sequence as a Lehmer code or (almost equivalently) as an inversion table.


title: Permutation

text: In the Lehmer code for a permutation "σ", the number "d" represents the choice made for the first term "σ", the number "d" represents the choice made for the second term


title: Permutation

text: "σ" among the remaining elements of the set, and so forth. More precisely, each "d" gives the number of "remaining" elements strictly less than the term "σ". Since those remaining elements are bound to turn up as some later term "σ", the digit "d" counts the "inversions" ("i","j") involving "i" as smaller index (the number of values "j" for which "i" < "j" and "σ" > "σ"). The inversion table for "σ" is quite similar, but here "d" counts the number of inversions ("i","j") where "k" = "σ" occurs as the smaller of the two values appearing in inverted order. Both encodings can be visualized by an "n" by "n" Rothe diagram (named after Heinrich August Rothe) in which dots at ("i","σ") mark the entries of the permutation, and a cross at ("i","σ") marks the inversion ("i","j"); by the definition of inversions a cross appears in any square that comes both before the dot ("j","σ") in its column, and before the dot ("i","σ") in its row. The Lehmer code lists the numbers of crosses in successive rows, while the inversion table lists the numbers of crosses in successive columns; it is just the Lehmer code for the inverse permutation, and vice versa.


title: Permutation

text: To effectively convert a Lehmer code "d", "d", ..., "d", "d" into a permutation of an ordered set "S", one can start with a list of the elements of "S" in increasing order, and for "i" increasing from 1 to "n" set "σ" to the element in the list that is preceded by "d" other ones, and remove that element from the list. To convert an inversion table "d", "d", ..., "d", "d" into the corresponding permutation, one can traverse the numbers from "d" to "d" while inserting the elements of "S" from largest to smallest into an initially empty sequence; at the step using the number "d" from the inversion table, the element from "S" inserted into the sequence at the point where it is preceded by "d" elements already present. Alternatively one could process the numbers from the inversion table and the elements of "S" both in the opposite order, starting with a row of "n" empty slots, and at each step place the element from "S" into the empty slot that is preceded by "d" other empty slots.


title: Permutation

text: Converting successive natural numbers to the factorial number system produces those sequences in lexicographic order (as is the case with any mixed radix number system), and further converting them to permutations preserves the lexicographic ordering, provided the Lehmer code interpretation is used (using inversion tables, one gets a different ordering, where one starts by comparing permutations by the "place" of their entries 1 rather than by the value of their first entries). The sum of the numbers in the factorial number system representation gives the number of inversions of the permutation, and the parity of that sum gives the signature of the permutation. Moreover, the positions of the zeroes in the inversion table give the values of left-to-right maxima of the permutation (in the example 6, 8, 9) while the positions of the zeroes in the Lehmer code are the positions of the right-to-left minima (in the example positions the 4, 8, 9 of the values 1, 2, 5); this allows computing the distribution of such extrema among all permutations. A permutation with Lehmer code "d", "d", ..., "d", "d" has an ascent if and only if .


title: Permutation

text: In computing it may be required to generate permutations of a given sequence of values. The methods best adapted to do this depend on whether one wants some randomly chosen permutations, or all permutations, and in the latter case if a specific ordering is required. Another question is whether possible equality among entries in the given sequence is to be taken into account; if so, one should only generate distinct multiset permutations of the sequence.


title: Permutation

text: An obvious way to generate permutations of "n" is to generate values for the Lehmer code (possibly using the factorial number system representation of integers up to "n"!), and convert those into the corresponding permutations. However, the latter step, while straightforward, is hard to implement efficiently, because it requires "n" operations each of selection from a sequence and deletion from it, at an arbitrary position; of the obvious representations of the sequence as an array or a linked list, both require (for different reasons) about "n"/4 operations to perform the conversion. With "n" likely to be rather small (especially if generation of all permutations is needed) that is not too much of a problem, but it turns out that both for random and for systematic generation there are simple alternatives that do considerably better. For this reason it does not seem useful, although certainly possible, to employ a special data structure that would allow performing the conversion from Lehmer code to permutation in "O"("n" log "n") time.


title: Permutation

text: For generating random permutations of a given sequence of "n" values, it makes no difference whether one applies a randomly selected permutation of "n" to the sequence, or chooses a random element from the set of distinct (multiset) permutations of the sequence. This is because, even though in case of repeated values there can be many distinct permutations of "n" that result in the same permuted sequence, the number of such permutations is the same for each possible result. Unlike for systematic generation, which becomes unfeasible for large "n" due to the growth of the number "n"!, there is no reason to assume that "n" will be small for random generation.


title: Permutation

text: The basic idea to generate a random permutation is to generate at random one of the "n"! sequences of integers "d","d"...,"d" satisfying (since "d" is always zero it may be omitted) and to convert it to a permutation through a bijective correspondence. For the latter correspondence one could interpret the (reverse) sequence as a Lehmer code, and this gives a generation method first published in 1938 by Ronald Fisher and Frank Yates.


title: Permutation

text: While at the time computer implementation was not an issue, this method suffers from the difficulty sketched above to convert from Lehmer code to permutation efficiently. This can be remedied by using a different bijective correspondence: after using "d" to select an element among "i" remaining elements of the sequence (for decreasing values of "i"), rather than removing the element and compacting the sequence by shifting down further elements one place, one swaps the element with the final remaining element. Thus the elements remaining for selection form a consecutive range at each point in time, even though they may not occur in the same order as they did in the original sequence. The mapping from sequence of integers to permutations is somewhat complicated, but it can be seen to produce each permutation in exactly one way, by an immediate induction. When the selected element happens to be the final remaining element, the swap operation can be omitted. This does not occur sufficiently often to warrant testing for the condition, but the final element must be included among the candidates of the selection, to guarantee that all permutations can be generated.


title: Permutation

text: The resulting algorithm for generating a random permutation of codice_1 can be described as follows in pseudocode:


title: Permutation

text: If "d" = "i", the first assignment will copy an uninitialized value, but the second will overwrite it with the correct value "i".


title: Permutation

text: However, Fisher-Yates is not the fastest algorithm for generating a permutation, because Fisher-Yates is essentially a sequential algorithm and "divide and conquer" procedures can achieve the same result in parallel.


title: Permutation

text: One classic, simple, and flexible algorithm is based upon finding the next permutation in lexicographic ordering, if it exists. It can handle repeated values, for which case it generates each distinct multiset permutation once. Even for ordinary permutations it is significantly more efficient than generating values for the Lehmer code in lexicographic order (possibly using the factorial number system) and converting those to permutations. It begins by sorting the sequence in (weakly) increasing order (which gives its lexicographically minimal permutation), and then repeats advancing to the next permutation as long as one is found. The method goes back to Narayana Pandita in 14th century India, and has been rediscovered frequently.


title: Permutation

text: The following algorithm generates the next permutation lexicographically after a given permutation. It changes the given permutation in-place.


title: Permutation

text: For example, given the sequence [1, 2, 3, 4] (which is in increasing order), and given that the index is zero-based, the steps are as follows:


title: Permutation

text: Following this algorithm, the next lexicographic permutation will be [1, 3, 2, 4], and the 24th permutation will be [4, 3, 2, 1] at which point "a"["k"] < "a"["k" + 1] does not exist, indicating that this is the last permutation.


title: Permutation

text: This method uses about 3 comparisons and 1.5 swaps per permutation, amortized over the whole sequence, not counting the initial sort.


title: Permutation

text: An alternative to the above algorithm, the Steinhaus–Johnson–Trotter algorithm, generates an ordering on all the permutations of a given sequence with the property that any two consecutive permutations in its output differ by swapping two adjacent values. This ordering on the permutations was known to 17th-century English bell ringers, among whom it was known as "plain changes". One advantage of this method is that the small amount of change from one permutation to the next allows the method to be implemented in constant time per permutation. The same can also easily generate the subset of even permutations, again in constant time per permutation, by skipping every other output permutation.


title: Permutation

text: An alternative to Steinhaus–Johnson–Trotter is Heap's algorithm, said by Robert Sedgewick in 1977 to be the fastest algorithm of generating permutations in applications.


title: Permutation

text: The following figure shows the output of all three aforementioned algorithms for generating all permutations of length formula_169, and of six additional algorithms described in the literature.


title: Permutation

text: Meandric systems give rise to "meandric permutations", a special subset of "alternate permutations". An alternate permutation of the set {1, 2, ..., 2"n"} is a cyclic permutation (with no fixed points) such that the digits in the cyclic notation form alternate between odd and even integers. Meandric permutations are useful in the analysis of RNA secondary structure. Not all alternate permutations are meandric. A modification of Heap's algorithm has been used to generate all alternate permutations of order "n" (that is, of length 2"n") without generating all (2"n")! permutations. Generation of these alternate permutations is needed before they are analyzed to determine if they are meandric or not.


title: Permutation

text: The algorithm is recursive. The following table exhibits a step in the procedure. In the previous step, all alternate permutations of length 5 have been generated. Three copies of each of these have a "6" added to the right end, and then a different transposition involving this last entry and a previous entry in an even position is applied (including the identity; that is, no transposition).


title: Permutation

text: Permutations are used in the interleaver component of the error detection and correction algorithms, such as turbo codes, for example 3GPP Long Term Evolution mobile telecommunication standard uses these ideas (see 3GPP technical specification 36.212).


title: Permutation

text: Such applications raise the question of fast generation of permutations satisfying certain desirable properties. One of the methods is based on the permutation polynomials. Also as a base for optimal hashing in Unique Permutation Hashing.


title: Ghostbusters (franchise)

text: The Ghostbusters franchise consists of American supernatural horror-comedies, based on an original concept created by Dan Aykroyd and Harold Ramis in 1984. The plot ostensibly centers around a group of eccentric New York City scientists who investigate, encounter, and capture ghosts, paranormal manifestations, demigods and demons. The franchise expanded with licensed action figures, books, comic books, video games, television series, theme park attractions, and other original "Ghostbusters"-themed products.


title: Ghostbusters (franchise)

text: The Ghostbusters use a specialized set of equipment in the 1984 film, and all subsequent "Ghostbusters" fiction includes similar equipment to aid in the capture and containment of ghosts. In addition to the main technology used in the series, a script draft for "Ghostbusters III" includes the Ghostbusters developing a machine to transport themselves to an alternate Manhattan to save New York.


title: Ghostbusters (franchise)

text: "Ghostbusters", the first film in the series, is a 1984 sci-fi comedy film about three New York City scientists. After they are fired from Columbia University, they start their own business investigating and capturing ghosts. Starring Bill Murray, Dan Aykroyd, Harold Ramis, Rick Moranis, Sigourney Weaver, Annie Potts, and Ernie Hudson, it was released in the United States on June 8, 1984. It had been made on a budget, but it grossed approximately in the United States and over abroad during its theatrical run, more than the domestic gross of the second "Indiana Jones" installment, making it the most successful film in America that year (after re-releases), and one of the most successful comedies of the 1980s. The American Film Institute ranked it 28th in its list of the top 100 comedies of all time. IGN voted "Ghostbusters" the greatest comedy ever in 2005. The TV Channel Bravo ranked "Ghostbusters" number 28 on their "100 Funniest Movies" list in 2006.


title: Ghostbusters (franchise)

text: The second film, "Ghostbusters II", was released on June 16, 1989. Taking place five years after the first, the Ghostbusters have lost their credibility due to the amount of property damage they have caused, but identify a new threat to New York City after discovering a river of ectoplasmic slime that reacts to the great deal of negative emotions within the city. Murray, Aykroyd, Ramis, Hudson, Weaver, Potts, and Moranis reprised their roles from the first film, and were joined by Peter MacNicol and Wilhelm von Homburg, among others. After the success of the first film and the animated series "The Real Ghostbusters", Columbia Pictures pressed the producers to make a sequel. Aykroyd, Ramis, and Reitman were uncomfortable with this at first, as the original film was intended to be conclusive and they wished to work on other projects. Eventually, they agreed and created a script. The sequel earned off a budget, but received lukewarm reviews compared to the first film.


title: Ghostbusters (franchise)

text: The third film, "Ghostbusters: Afterlife", was released on November 19, 2021. Taking place thirty-two years after the second, the Ghostbusters have disbanded and their legacy is mostly forgotten. After a single mother and her children move to an Oklahoma farm they inherited from her estranged father, Egon Spengler, who went on a mission to prevent an apocalypse. The film was directed by Jason Reitman, son of original director Ivan Reitman, with a script co-written by himself and Gil Kenan, while Ivan Reitman served as a producer. The cast includes Mckenna Grace, Finn Wolfhard, Carrie Coon and Paul Rudd, and were joined by Logan Kim and Celeste O'Connor, among others. Additionally, Murray, Aykroyd, Hudson, Potts and Weaver appear in supporting roles, reprising their characters from the first two films.


title: Ghostbusters (franchise)

text: In December 2021, Dan Aykroyd expressed interest in having the surviving three actors of the original "Ghostbusters" team reprise their roles in up to three additional sequels. On the possibility of sequels, David A. Gross of "Franchise Entertainment Research" felt that "Afterlife" performed well enough at the box office for Sony to pursue additional films.


title: Ghostbusters (franchise)

text: In April 2022 at CinemaCon, a fourth film was announced to be in early development. The project will serve as a sequel to "Ghostbusters: Afterlife". Jason Reitman said this film would continue to follow the Spengler family, with the working title being called "Firehouse". In June, Sony announced the release date of December 20, 2023.


title: Ghostbusters (franchise)

text: The 2016 film, "Ghostbusters", is a relaunch of the franchise which takes place in an alternate universe, featuring a new cast of characters, but follows a similar narrative as the original film. A group of eccentric researchers make discoveries within paranormal incidents with their intentions being to detect and capture ghosts, and protect New York City from those spirits. The film principally features a new cast, starring Kristen Wiig, Melissa McCarthy, Leslie Jones and Kate McKinnon as the all-female Ghostbuster team, along with Chris Hemsworth as their male receptionist. Additionally, Aykroyd, Murray, Weaver, Hudson and Potts all had small cameo roles. The film was released on July 15, 2016, as "Ghostbusters", with the home media released being rebranded to "Ghostbusters: Answer the Call". It received mixed reviews, and grossed off a budget, after accounting for marketing, a $70 million loss.


title: Ghostbusters (franchise)

text: In October 2015, Ivan Reitman announced that he was producing an animated film for Sony Pictures Animation, with Fletcher Moules attached to the project as both animator and director. The film will tell a story from the perspective of ghosts. The film will begin production following the completion and release of "Ghostbusters: Afterlife". The project was reconfirmed in June 2022, with Jennifer Kluska and Chris Prynoski as directors and Brenda Hsueh as the writer of the film.


title: Ghostbusters (franchise)

text: In December 2014, the Sony Pictures hack revealed that an action-comedy spin-off film, centered around another team of Ghostbusters was in development. Channing Tatum, Reid Carolin, and the Russo brothers pitched the movie to the studio, and was confirmed to supplement and be in development simultaneously with Paul Feig's "Ghostbusters: Answer the Call", and intended to be the first installment in a series of films inspired by Christopher Nolan's "The Dark Knight Trilogy". Tatum was being courted to star in the film, with Chris Pratt viewed as his potential co-star. By March 2015, the film was officially confirmed to be in active-development. Written by Drew Pearce, the film was seen as an expansion of the "Ghostbusters" multiverse. Ivan Reitman described its development as being in line with the plans and production bible that they had created thirty years prior during the original film; the purpose of the project was "to build the "Ghostbusters" into the universe it always promised it might become". Joe and Anthony Russo were in early negotiations to direct the film. Ivan Reitman, the Russo brothers, Channing Tatum, Reid Carolin, and Peter Kiernan were to serve as producers. By June however, Tatum confirmed that the project had been delayed in favor of other projects.


title: Ghostbusters (franchise)

text: In February 2022, Phil Lord and Christopher Miller announced that they had been attached to the project during its development stages, also saying that there is still potential at the studio that the film will be green-lit in the future.


title: Ghostbusters (franchise)

text: From 1986 to 1991, Columbia Pictures Television and DIC Entertainment produced an animated spin-off television series created by Harold Ramis and Dan Aykroyd, entitled "The Real Ghostbusters". "The Real" was added to the title due to a dispute with Filmation and its "Ghostbusters" properties. The series continues the adventures of paranormal investigators Venkman, Stantz, Spengler, Zeddemore, their secretary Melnitz, and their mascot ghost Slimer. "The Real Ghostbusters" was nominated for an Emmy.


title: Ghostbusters (franchise)

text: When the show's producers began to see the youth appeal of the character Slimer, he began to be featured more prominently. In 1988, the series was retooled and renamed "Slimer! and the Real Ghostbusters", and featured an hour-long format with a typical "Real Ghostbusters" episode leading into a more kid-friendly "Slimer!" cartoon. As the series progressed, the regular "Real Ghostbusters" episodes started to become lighter in tone so as not to frighten the growing fanbase of young children. Additionally, the characterizations became more one-dimensional, and the animation became less detailed. More changes went on behind the scenes as well with the departure of writer J. Michael Straczynski. Dave Coulier of "Full House" fame came on to fill the role of Peter (voiced by Lorenzo Music), Buster Jones took over Winston from Arsenio Hall, and Kath Soucie took on Janine after Laura Summer voiced the role. Straczynski returned to the series temporarily in the 1990 season. The only cast members who remained throughout the entire series were Frank Welker (voice of Stantz and Slimer) and Maurice LaMarche (voice of Spengler). The show was cancelled in 1991.


title: Ghostbusters (franchise)

text: "Extreme Ghostbusters" was a sequel and spin-off of "The Real Ghostbusters" that aired in late 1997. The show featured a new team of younger Ghostbusters led by veteran Ghostbuster Egon Spengler, secretary Janine Melnitz, and the ghost Slimer. The premise is similar to the plot of "Ghostbusters II". Set years after the end of "The Real Ghostbusters", a lack of supernatural activity has put the Ghostbusters out of business. Each has gone his separate way, except for Egon, who still lives in the Firehouse to monitor the containment unit, further his studies, and teach a class on the paranormal at a local college. When ghosts start to reappear, Egon is forced to recruit his four students as the new Ghostbusters. The new Ghostbusters were Kylie Griffin, a genius, expert on the occult, and female counterpart to Egon; Eduardo Rivera, a hip, cynical Latino slacker and counterpart to Peter; Garrett Miller, a wheelchair-bound young athlete and counterpart to Winston; and Roland Jackson, a studious African-American machinery whiz and counterpart to Ray. The show was given the Los Angeles Commission on Disabilities Award for making one of its main characters (Garrett) disabled, but universally relatable.


title: Ghostbusters (franchise)

text: In June 2016, a new animated series titled, "Ghostbusters: Ecto Force", was announced to be in development, with an initial targeted release of early-2018. The series was to be set in the year 2050, following a new team of Ghostbusters who capture ghosts from around the world. In August 2017, Reitman revealed that the series had been postponed to prioritize development on the planned "Ghostbusters" animated spin-off film.


title: Ghostbusters (franchise)

text: An animated streaming television series by Netflix was announced in June 2022. The series will be produced by Jason Reitman and Gil Kenan, both who produced "Ghostbusters: Afterlife", and as a production of Ghost Corps and Sony Pictures Animation.