报告题目：Equivariant inverse Z-polynomials of matroids

报 告 人：郜璐璐 副教授（西北工业大学）

报告时间：2026年10月28日（星期三）15:00—16:00

报告地点：线上报告，腾讯会议：157-965-002

校内联系人：毛建玺 副教授         联系方式：84708351-8604

报告摘要：In this talk, I will discuss the equivariant inverse Z-polynomial of a matroid equipped with an action of a finite group. We prove that the coefficients of the equivariant inverse Z-polynomials are honest representations and that these polynomials are palindromic. Explicit formulas are obtained for uniform matroids equipped with the action of the symmetric group. The corresponding formulas for q-niform matroids are derived using the Comparison Theorem for unipotent representations. We show that these polynomials are equivariantly unimodal and strongly inductively log-concave for both uniform and q-niform matroids. For arbitrary equivariant paving matroids, explicit expressions are obtained by relating the polynomials of a matroid to those of its relaxation. This is joint work with Yun Li and Matthew H. Y. Xie.

报告人简介：郜璐璐，西北工业大学准聘副教授，硕士生导师。2017年博士毕业于南开大学组合数学中心，导师为杨立波教授。研究方向为代数组合学，具体涉及对称函数理论、组合多项式理论和有限群表示论等。发表科研论文20余篇，主要发表于J. Comb. Theory Ser. A、J. Comb. Theory Ser. B、J. Comb. Algebra、SIAM J. Discrete Math.、Proc. Amer. Math. Soc.等期刊上。主持国家自然科学基金青年、面上项目、国家外专项目等3项，主持省部级科研项目3项。目前担任中国数学会计算机数学专业委员会委员。