Cyclic descents, matchings and Schur-positivity (2210.14839v2)

Published 26 Oct 2022 in math.CO

Abstract: 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 explicit cyclic descent extensions on involutions, standard Young tableaux and Motzkin paths. Schur-positivity of the associated quasisymmetric functions follows.

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