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Vassilis Moustakas:Euler-Mahonian identities and specializations of quasisymmetric functions

Time: Wed 2022-09-21 10.15 - 11.15

Location: Zoom Meeting ID: 637 4378 6038 (please contact any of the organizers for the password)

Abstract: A combinatorial permutation statistic is called Eulerian (resp. Mahonian) if it has the same distribution with the number of descents (resp. major index). The generating polynomials of pairs of an Eulerian and a Mahonian statistic satisfy rational generating function identities which are called Euler-Mahonian identities. In recent years, many researchers have studied generalizations of Euler-Mahonian statistics to real and complex reflection groups (including colored permutation groups). In this talk, we aim to review Euler--Mahonian pairs of statistics on colored permutations and develop a systematic way of proving general formulas for their generating polynomials by specializing Poirier's colored quasisymmetric functions. We will then apply these formulas to prove Euler-Mahonian identities on colored permutations, derangements and involutions.