Seminars & Colloquia Calendar
Cyclic permutations, shuffles, and quasi-symmetric functions
Ron Adin, Bar Ilan University
Date & time: Thursday, 04 February 2021 at 5:00PM - 6:00PM
Abstract: Richard Stanley proved that the distribution of descent number over all the shuffles of two permutations depends only on the descent numbers of the permutations.
We present an explicit cyclic analogue of this result. The tools used for the proof include a new cyclic counterpart of Gessels quasi-symmetric functions, an unusual ring homomorphism, and a mysterious binomial identity with an interesting history.
Based on joint work with Ira Gessel, Vic Reiner, and Yuval Roichman.
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420