On cyclic descents for tableaux
Combinatorics
2017-11-27 v2
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.
Cite
@article{arxiv.1710.06664,
title = {On cyclic descents for tableaux},
author = {Ron M. Adin and Victor Reiner and Yuval Roichman},
journal= {arXiv preprint arXiv:1710.06664},
year = {2017}
}
Comments
31 pages, minor changes