Strictness of the log-concavity of generating polynomials of matroids

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:181

Article

Muraia, Satoshi¹  Nagaoka, Takahiro²  Yazawac, Akiko³ 

[1] Waseda Univ, Fac Educ, Dept Math, Shinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan

[2] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto 6068522, Japan

[3] Shinshu Univ, Grad Sch Med Sci & Technol, Dept Sci & Technol, Matsumoto, Nagano 3908621, Japan

关键词: Matroid;    Independent set;    Mason's conjecture;    Lorentzian polynomial;    Hodge-Riemann relation;    Morphism of matroids;   

DOI  :  10.1016/j.jcta.2020.105351

来源: Elsevier

【 摘 要 】

Recently, it was proved by Anari-Oveis Gharan-Vinzant, Anari-Liu-Oveis Gharan-Vinzant and Branden-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. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free