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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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