I was struggling with this paper about codes which can correct single deletion and re-ranking in permutations, http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6875337[Published in:Information Theory (ISIT), 2014 IEEE International Symposium onDate of Conference:June 29 2014-July 4 2014, Page(s):    2764 - 2768 INSPEC Accession Number:    14515064, Conference Location :    Honolulu, HI DOI:    10.1109/ISIT.2014.6875337 Publisher:    IEEE] I wonder if there is a longer and more explained version of Theorem 2 in this paper.Or is there any other paper which explains this better?  The Theorem 2 at the end is extremely difficult to follow!For example at the top of the second column in page 5 even the authors state things like it is straightforward (but tedious) to see that the set of possible values for x is exactly $\{u,u+1,..,v+1\}$. Can someone help understand this? Many of the things towards the end were not easy to follow : like why is $\{\sigma_i,..,\sigma_j\}$ an increasing run of $\sigma$ and why is $\{p,p+1,..,q\}$ an increasing sub-sequence of $\sigma$. The above is not looking obvious from the initial definition : In the beginning the $i$ and $j$ were defined such that from position $i$ to $j$ in the signature vector of the permutation $\pi$ is a sequence of $1$s. And $p$ and $q$ were initially defined such that from the position $p$ to $q$ is a sequence of $1$s in the signature vector of the permutation $\pi^{-1}$. And $\sigma$ is a permutation obtained from $\pi$ after a single deletion and re-ranking. 
Codes for correcting a single deletion and re-ranking of a permutation
error correcting codes;code generation