Monotonicity for generalized binomial coefficients and Jack positivity
Combinatorics
2025-08-11 v1 Quantum Algebra
Representation Theory
Abstract
Binomial formulas for Schur polynomials and Jack polynomials were studied by Lascoux in 1978, and Kaneko, Okounkov--Olshanski and Lassalle in the 1990s. We prove that the associated binomial coefficients are monotone and derive some symmetric function inequalities, in particular, a Schur positivity and Jack positivity result. These inequalities are similar to those studied by Newton, Muirhead, Gantmacher, Cuttler--Greene--Skandera, Sra and Khare--Tao.
Cite
@article{arxiv.2508.05759,
title = {Monotonicity for generalized binomial coefficients and Jack positivity},
author = {Hong Chen and Siddhartha Sahi},
journal= {arXiv preprint arXiv:2508.05759},
year = {2025}
}
Comments
Accepted for poster presentation at FPSAC 2025