报告题目：The homogeneous little q-Jacobi polynomials

报告摘要：Motivated by the $q$-operational equation for Rogers--Szeg\"{o} polynomials [Sci. China Math. {\bf 66}(2023), no. 6, 1199--1216.], it is natural to ask whether some general $q$-polynomials exist, which are solutions of certain $q$-operational equations, $q$-difference equations and $q$-partial differential equations. In this paper, based on the importance of little $q$-Jacobi polynomials, we define two homogeneous little $q$-Jacobi polynomials and search their corresponding $q$-operational equations, $q$-difference equations and $q$-partial differential equations by the technique of noncommutative $q$-binomial theorem and recurrence relations. In addition, we deduce some generating functions for homogeneous little $q$-Jacobi polynomials by methods of $q$-operational equation, $q$-difference equation and $q$-partial differential equation. Moreover, we consider recurrence relations for homogeneous little $q$-Jacobi polynomials.

报告人简介：曹健，杭州师范大学教授，硕士生导师，从事组合数学与特殊函数领域的研究，主持国家及浙江省基金等多项，已在本领域(Stud. Appl. Math.、Adv. Appl. Math.、Math. Nachr.、Bull. Sci. Math.等)重要学术刊物上以独立或通讯作者发表40余篇SCI论文，入选杭州市属高校中青年学术带头人、杭州市“131”人才等，多次在中国数学会学术年会、全国组合数学与图论、英国肯特大学及伦敦大学学院等国内外学术会议上作报告。

报告时间：2025年12月1日 14：30-15：30

报告地点：腾讯会议 856 362 132

报告题目：Counting alternating runs via Hetyei-Reiner trees

报告摘要：The generating polynomial of all $n$--permutations with respect to the number of alternating runs possesses a root at $-1$ of multiplicity $\lfloor (n-2)/2\rfloor$ for$n\ge2$. This fact can be deduced by combining the David--Barton formula for Eulerian polynomials with the Foata--Schützenberger $\gamma$--decomposition of these polynomials. Recently, Bóna provided a group--action proof of this result. In this talk, I propose an alternative approach based on the Hetyei--Reiner action on binary trees, which yields a new combinatorial interpretation of Bóna’s quotient polynomial. Furthermore, we extend our study to analogous results for permutations of types~B and~D. As a consequence of our bijective framework, we also obtain combinatorial proofs of David--Barton type identities for permutations of types~A and~B. This talk is based on a joint work with Yunze Wang and Jiang Zeng.

报告人简介：潘琼琼，2020年博士毕业于法国里昂大学，2021年入职温州大学，主要研究计数组合学以及正交多项式理论。多篇论文发表在JCTA、AAM、DM、EJC等组合数学领域国际期刊上，目前主持一项国家自然科学基金青年项目。

报告时间：2025年12月1日 15：30-16：30

报告地点：腾讯会议 856 362 132

报告题目：Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids

报告摘要：In this talk, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite graphs $K_{1,1,n}$. These polynomials were introduced by Proudfoot as an extension of the Kazhdan--Lusztig theory for matroids. We derive closed-form expressions for the $S_n$-equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids and present them explicitly in terms of the irreducible representations of $S_n$. As an application, we also provide explicit formulas for the non-equivariant inverse Kazhdan--Lusztig polynomials, originally defined by Gao and Xie, and give an alternative proof using generating functions. Furthermore, we prove that the inverse Kazhdan--Lusztig polynomials of thagomizer matroids are log-concave.

报告人简介：郜璐璐，西北工业大学副教授。毕业于南开大学组合数学中心，师从杨立波教授。研究方向为代数组合学，主要包括拟阵多项式理论、对称函数理论等，在JCTB、Siam 离散、Proceedings AMS等期刊上发表科研论文近二十篇。报告时间：2025.3.9 15:00-16:00

报告时间：2025年12月2日 9：00-10：00

报告地点：腾讯会议 674 428 130

报告题目：Characteristic Polynomials of Deformed Braid Arrangements

报告摘要：A hyperplane arrangement is a finite set of hyperplanes (codimension-one affine subspaces) in a real vector space. An especially important arrangement is the braid arrangement, which consists of all hyperplanes in . In this talk, we consider a specific type of deformation of the braid arrangement in , given by , where is a finite set of real numbers. We provide an explicit expression for the characteristic polynomial of in terms of the number of regions of each level . In particular, if and for non-negative integers and with , we show that the characteristic polynomial of has a single real root 0 of multiplicity one when is odd, and has one more real root of multiplicity one when is even.

报告人简介：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。

报告时间：2025年12月2日 10：00-11：00

报告地点：腾讯会议 674 428 130