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arXiv · 2508.05759

Monotonicity for generalized binomial coefficients and Jack positivity

Hong Chen·Siddhartha Sahi
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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.

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Hong Chen, Siddhartha Sahi. 2025-08-07. Monotonicity for generalized binomial coefficients and Jack positivity. https://arxiv.org/abs/2508.05759

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