Cyclic Descents, Matchings and Schur-Positivity

Abstract

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