Séminaire Lotharingien de Combinatoire, 80B.60 (2018), 12 pp.

Ron M. Adin, Victor Reiner, and Yuval Roichman

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.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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