Speaker: Ron Adin, Bar-Ilan University
Title: Cyclic permutations, shuffles and quasi-symmetric functions
Abstract:
By a theorem of Stanley, the distribution of descent number over all the shuffles of two permutations depends only on the descent numbers of these permutations. For a quantitative version of this result and its cyclic analogue, we use a new cyclic counterpart of Gessel's ring of quasi-symmetric functions, together with an unusual homomorphism and a mysterious binomial identity.
No previous acquaintance assumed.
Based on the recent preprint arXiv:1811.05440; joint work with Ira Gessel, Vic Reiner and Yuval Roichman.