报告时间：2026年5月15日（周五）上午 9:30-10:15，10:30-11:15
报告地点：苏州大学天赐庄校区精正楼103报告厅
报告人：何天晓（Tian-Xiao He） 教授，Illinois Wesleyan University, USA
报告摘要：
In this talk, we introduce Riordan arrays, multiple Riordan arrays, and multiple almost-Riordan arrays using combinatorial object enumeration and lattice paths. All Riordan arrays, all multiple Riordan arrays, and all double approximate Riordan arrays constitute three groups, respectively called the Riordan group, the multiple Riordan group, and the multiple approximate Riordan group. We also present the sequence characteristics of these Riordan arrays and their production matrices. We define the compression of multiple Riordan arrays and multiple almost-Riordan arrays and give their sequence characteristics. We investigate the total positivity of the compression of multiple Riordan arrays and multiple almost-Riordan arrays. Finally, we discuss the representation of the orthogonal polynomial sequence and its three-dimensional extension using the production matrices of the corresponding Riordan arrays. Time permitting, we will propose the embeddability of Coxeter groups to Riordan groups, as well as a unified combinatorial and algebraic framework connecting wavelet systems and Riordan group operators.
报告人简介：
何天晓教授，1988年和1991年分别在大连理工大学和德克萨斯农工大学（卡城校区）获得了博士学位。自2000年起至今，何天晓教授担任伊利诺伊卫斯理大学数学教授；2013年起至今，担任伊利诺伊卫斯理大学自然科学与数学的贝尔林（Earl and Marian A. Beling）教授。何天晓教授先后出任10多个国际数学会议的组织委员会委员。目前，他单独或合作发表了140篇数学研究论文和出版6部数学专著，并长期担任9种数学期刊的编辑或主编。
邀请人：马欣荣