The catenary degrees of elements in numerical monoids generated by arithmetic sequences
ABSTRACTWe compute the catenary degree of elements contained in numerical monoids generated by arithmetic sequences. We find that this can be done by describing each element in terms of the cardinality of its length set and of its set of factorizations. As a corollary, we find for such monoids that the catenary degree becomes fixed on large elements. This allows us to define and compute the dissonance number- the largest element with a catenary degree different from the fixed value. We determine the dissonance number in terms of the arithmetic sequence’s starting point and its number of generators.
As a result of the first study on secondary metabolites from the cosmopolitan bioluminescent marine tube polychaete Chaetopterus variopedatus, a new bicyclic guanidine alkaloid, 6-epi-monanchorin (1), along with the previously known monanchorin (2) were isolated. The structure of 1 was elucidated by...