On cyclic descents for tableaux

Ron M. Adin, Victor Reiner, Yuval Roichman

Research output: Contribution to conferencePaperpeer-review

Abstract

The notion of descent set, for permutations as well as for standard Young tableaux (SYT), is classical. Cellini introduced a natural notion of cyclic descent set for permutations, and Rhoades introduced such a notion for SYT - but only for rectangular shapes. In this work we define cyclic extensions of descent sets in a general context, and prove existence and essential uniqueness for SYT of almost all shapes. The proof applies nonnegativity properties of Postnikov's toric Schur polynomials, providing a new interpretation of certain Gromov-Witten invariants.

Original languageEnglish
StatePublished - 2018
Event30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States
Duration: 16 Jul 201820 Jul 2018

Conference

Conference30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/TerritoryUnited States
CityHanover
Period16/07/1820/07/18

Keywords

  • Cyclic descent
  • Descent
  • Gromov-Witten invariant
  • Ribbon Schur function
  • Standard Young tableau

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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