Cyclic descents, matchings and Schur-positivity

Ron M. Adin; Yuval Roichman

doi:10.37236/11761

Cyclic descents, matchings and Schur-positivity

Ron M. Adin, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

A new descent set statistic on involutions, defined geometrically via their inter-pretation 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.

Original language	English
Article number	#P2.41
Journal	Electronic Journal of Combinatorics
Volume	30
Issue number	2
DOIs	https://doi.org/10.37236/11761
State	Published - 2023

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/11761

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title = "Cyclic descents, matchings and Schur-positivity",

abstract = "A new descent set statistic on involutions, defined geometrically via their inter-pretation 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.",

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AB - A new descent set statistic on involutions, defined geometrically via their inter-pretation 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.

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U2 - 10.37236/11761

DO - 10.37236/11761

M3 - مقالة

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VL - 30

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

M1 - #P2.41

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Cyclic descents, matchings and Schur-positivity

Abstract

All Science Journal Classification (ASJC) codes

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