Symmetry of the generating function of semistandard oscillating tableaux
Combinatorics
2026-01-27 v1
Abstract
H.Choi-D.Kim-S.J.Lee and S.J.Lee introduced a new kind of tableaux, semistandard oscillating tableaux (SSOT), around 2024 in the context of Lusztig -weight multiplicities, KR crystals and King tableaux. In this paper, we study generating function of the SSOTs and its symmetry. First, we extend Gessel's and Assaf-Searles' expansion of a Schur function in terms of fundamental quasi-symmetric functions to our generating function. As a consequence, we show that it is -positive. Further, we improve Sundaram's work on oscillating tableaux by proving that it is symmetric, Schur-positive, and has Saturated Newton polytope.
Keywords
Cite
@article{arxiv.2601.17603,
title = {Symmetry of the generating function of semistandard oscillating tableaux},
author = {Masato Kobayashi and Tomoo Matsumura and Shogo Sugimoto},
journal= {arXiv preprint arXiv:2601.17603},
year = {2026}
}
Comments
26 pages