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arXiv · 1710.06664

On cyclic descents for tableaux

Ron M. Adin·Victor Reiner·Yuval Roichman
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Abstract

The notion of descent set, for permutations as well as for standard Young tableaux (SYT), is classical. Cellini introduced a natural notion of {\em cyclic descent set} for permutations, and Rhoades introduced such a notion for SYT --- but only for rectangular shapes. In this work we define {\em 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.

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Ron M. Adin, Victor Reiner, Yuval Roichman. 2017-11-22. On cyclic descents for tableaux. https://arxiv.org/abs/1710.06664

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