Cyclic descents, matchings and Schur-positivity

Ron M. Adin, Yuval Roichman

Published 2022-10-26Version 1

A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, is introduced in this paper, and shown to be equi-distributed with the standard one. This concept is then applied to construct an explicit cyclic descent extensions on involutions, standard Young tableaux and Motzkin paths. Schur-positivity of associated quasi-symmetric functions follows.