讲座题目：Characteristic Polynomials of Semimatroids

主办单位：数理学院/三峡数学研究中心

报告专家：符厚山

报告时间：12 月 18 日 14:00

报告地点：腾讯会议：410-966-193

报告摘要：A semimatroid can be thought of as a matroid-theoretic abstraction of the dependence properties of an affine hyperplane arrangement. In this talk, we extend the theory of characteristic polynomials—originally developed for hyperplane arrangements and matroids—to the semimatroid. Notably, we provide a combinatorial interpretation for the characteristic polynomial’s coefficients, which generalizes Whitney’s Broken Circuit Theorem to semimatroids. Furthermore, we demonstrate that the unsigned coefficients of this polynomial form a unimodal and log-concave sequence. Finally, we explore the connections between semimatroids, matroids, hyperplane arrangements, and graph colorings, with a particular focus on their characteristic polynomials.

专家简介：符厚山，广州大学数学与信息科学学院讲师。2018 年硕士毕业于中南大学（导师：周岳教授），2022 年博士毕业于湖南大学（导师：王岁杰教授），随后进入广州大学数学与信息科学学院，跟随唐春明教授从事博士后研究，2024 年出站并留校任教。主要从事超平面配置与拟阵的组合理论研究，重点关注其中的计数组合、组合分类及多项式不变量性质等方向,在 J. Combin. Theory Ser. A、Adv. Appl. Math、Discrete Math. 等权威数学期刊发表论文 10 余篇,主持国家自然科学青年基金 1 项。