报告题目：Coefficientwise total positivity of matrices enumerating rooted labeled trees

报告人：陈曦

负责人：李雪珊

报告时间：2025年10月09日14：30-15:30

报告地点：腾讯会议，会议号：946 975 419

参加人员：教师，研究生

报告摘要：In this talk we study three combinatorial models for the lower-triangular matrix with entries $\binom{n}{k}n^{n-k}$: two involving rooted trees and one involving partial functional digraphs. We show that this matrix is totally positive and that the sequences of its row-generating polynomials is coefficientwise Hankel-totally positive. We then generalize the results to polynomials that count improper and proper edges, and study the coefficientwise total positivity of the matrices associated to them. This work is joint with Alan Sokal.

报告人简介：陈曦，大连理工大学数学科学学院副教授、博士生导师，密歇根州立大学、伦敦大学学院访问学者。2015年博士毕业于大连理工大学，研究方向为组合数学，研究兴趣包括组合矩阵的全正性、组合序列的解析性质等，成果发表在《Adv. in Appl. Math.》、《European J. Combin.》、《Discrete Math.》等期刊。主持国家自然科学基金2项。现任中国运筹学会图论组合分会理事、CSIAM图论组合及应用专委会委员。