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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