Danai Deligeorgaki: Canon Permutations

Abstract: We will discuss canon permutations and their generalizations. Canon permutations are a class of multiset permutations that arise by "shuffling" multiple copies of a permutation of [n]:={1,2...,n}. They were recently introduced by Elizalde, and are motivated by pattern-avoidance concepts such as (quasi-)Stirling permutations. Elizalde proved that the descent polynomial of canon permutations exhibits a surprising product structure; as a further consequence, it is palindromic. His proofs relied on constructing lengtly bijections and using tools from the theory of Dyck paths. In this talk, we will go through new direct proofs of these results that appear in recent work with Matthias Beck (arXiv:2410.03245), as well as generalizations, through the theory of (P,w)-partitions. Our generalizations include a class of permutations that we call dissonant canon permutations. We will discuss palindromicity of their corresponding descent polynomials and end with a conjecture regarding their coefficients when expressed in the gamma basis.