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 (US)
StatePublished - 2018
Event30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States
Duration: Jul 16 2018Jul 20 2018

Conference

Conference30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
CountryUnited States
CityHanover
Period7/16/187/20/18

Bibliographical note

Funding Information:
∗radin@math.biu.ac.il. Partially supported by by a MISTI MIT-Israel grant. †reiner@math.umn.edu. Partially supported by NSF grant DMS-1601961. ‡yuvalr@math.biu.ac.il. Partially supported by by a MISTI MIT-Israel grant.

Keywords

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

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