Cyclic quasi-symmetric functions

Ron M. Adin, Ira M. Gessel, Victor Reiner, Yuval Roichman

Research output: Contribution to conferencePaperpeer-review

Abstract

The ring of cyclic quasi-symmetric functions is introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; they arise as toric P-partition enumerators, for toric posets P with a total cyclic order. The associated structure constants are determined by cyclic shuffles of permutations. For every non-hook shape l, the coefficients in the expansion of the Schur function sl in terms of fundamental cyclic quasi-symmetric functions are nonnegative. The theory has applications to the enumeration of cyclic shuffles and SYT by cyclic descents.

Original languageEnglish
StatePublished - 2019
Event31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019 - Ljubljana, Slovenia
Duration: 1 Jul 20195 Jul 2019

Conference

Conference31st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2019
Country/TerritorySlovenia
CityLjubljana
Period1/07/195/07/19

Bibliographical note

Publisher Copyright:
© FPSAC 2019 - 31st International Conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

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