论文标题
生成矩形多项式的对数洞的严格性
Strictness of the log-concavity of generating polynomials of matroids
论文作者
论文摘要
最近，Anari-oveis Gharan-Vinzant，Anari-liu-oveis Gharan-Vinzant和Brändén-Huh证明了这一点，对于任何矩阵$ m $，其基础产生了多项式及其独立集产生的基于多项式的多项式是在正骨上的log-concave。使用这些，他们在矩阵上获得了一些组合不平等，包括强烈梅森的猜想解决方案。在本文中，我们研究了这些多项式的对数洞穴的严格性，并确定何时在这些组合不平等中保持平等。我们还考虑了我们的结果对矩形的形态的概括。
Recently, it was proved by Anari-Oveis Gharan-Vinzant, Anari-Liu-Oveis Gharan-Vinzant and Brändén-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.
