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arXiv · 2003.09568

Strictness of the log-concavity of generating polynomials of matroids

Satoshi Murai·Takahiro Nagaoka·Akiko Yazawa
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Abstract

Recently, it was proved by Anari-Oveis Gharan-Vinzant, Anari-Liu-Oveis Gharan-Vinzant and Br\"{a}nd\'{e}n-Huh that, for any matroid $M$, its basis generating polynomial and its independent set generating polynomial are log-concave on the positive orthant. Using these, they obtain some combinatorial inequalities on matroids including a solution of strong Mason's conjecture. In this paper, we study the strictness of the log-concavity of these polynomials and determine when equality holds in these combinatorial inequalities. We also consider a generalization of our result to morphisms of matroids.

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Satoshi Murai, Takahiro Nagaoka, Akiko Yazawa. 2020-03-21. Strictness of the log-concavity of generating polynomials of matroids. https://arxiv.org/abs/2003.09568

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