报告题目：Minors of a Class of Recursive Matrices Related to Partial (x , y; a, b) - Motzkin Paths

报 告 人：孙怡东 教授 （大连海事大学）

报告时间：2025年8月25日（星期一）15:30-16:30

报告地点：数学科学学院624

校内联系人： 毛建玺 副教授     联系电话： 84708351-8604

报告摘要：The recursive matrices are closely related to many combinatorial objects and have been investigated intensively by many authors via continued fractions, orthogonal polynomials, generating functions, total positivity, etc. In this paper, we focus on the study of the weighted sums of $2 \times 2$ minors of particular recursive matrices $\mathcal{F}^{((1,1,1,\ldots)(x,y,y,\ldots),(a,b,b,\ldots))}$ by utilizing partial $(x,y; a,b)$-Motzkin paths. We also consider an alternating summation of weighted $2\times 2$ minors of the recursive matrix $\mathcal{F}^{((1,1,1,\ldots),(z+1,z+1,z+1,\ldots),(z+1,z,z,\ldots))}$ with the help of the residue theorem and the computer algebra package HolonomicFunctions. When the weight parameters $(x, y)$ and $(a, b)$ are specialized, several new identities are obtained related to some classical sequences involving Catalan numbers. Finally, we give some further comments and questions for the permanent case.

报告人简介：孙怡东，教授，现任大连海事大学理学院院长。主要研究方向为计数组合学、构造组合学等。先后在《European Journal of Combinatorics》《Electronic Journal of Combinatorics》《Discrete Mathematics》等组合数学国际知名杂志发表学术论文40余篇，其中SCI检索论文30余篇。主持完成国家自然科学基金项目2项，主持省部级项目及横向项目5项，参与国家级以及省级基金多项。指导研究生荣获辽宁省优秀硕士论文2人次。2009年入选辽宁省“百千万人才工程”千层人选；2018年09月至今担任大连市数学学会副理事长。2023年10月至今担任辽宁省数学会副理事长。