Krishna Menon: My descent(s) at KTH

Abstract: As clearly suggested by the title, I will be talking about two projects concerning descents in permutations that I've been working on during the past few months.

The first project is about descents in 'canon permutations'. These are objects that are constructed from a pair: a Dyck path and a permutation. By fixing a Dyck path and varying the permutation, we associate a descent polynomial to the Dyck path. We study these polynomials and find relations to known statistics on Dyck paths. This is based on ongoing work with Danai Deligeorgaki.

The second project is about longest subsequences in permutations with certain descent restrictions. This is motivated by Stanley's study of longest alternating subsequences in permutations. The main tool we use is the evacuation operation on standard Young tableaux. This is based on ongoing work with Anurag Singh.