On cyclic descents for tableaux

Ron M. Adin; Victor Reiner; Yuval Roichman

On cyclic descents for tableaux

Ron M. Adin, Victor Reiner, Yuval Roichman

Department of Mathematics

Bar-Ilan University

Research output: Contribution to conference › Paper › peer-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 language	English
State	Published - 2018
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: 16 Jul 2018 → 20 Jul 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	16/07/18 → 20/07/18

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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title = "On cyclic descents for tableaux",

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.",

keywords = "Cyclic descent, Descent, Gromov-Witten invariant, Ribbon Schur function, Standard Young tableau",

author = "Adin, {Ron M.} and Victor Reiner and Yuval Roichman",

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TY - CONF

T1 - On cyclic descents for tableaux

AU - Adin, Ron M.

AU - Reiner, Victor

AU - Roichman, Yuval

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Cyclic descent

KW - Descent

KW - Gromov-Witten invariant

KW - Ribbon Schur function

KW - Standard Young tableau

UR - http://www.scopus.com/inward/record.url?scp=85089347339&partnerID=8YFLogxK

M3 - محاضرة

T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

On cyclic descents for tableaux

Abstract

Conference

Keywords

All Science Journal Classification (ASJC) codes

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Cite this