温州大学数理学院2025年第11期数理大讲堂

题目：Variations of Eulerian polynomials and their gamma-positivity

报告人：曾江教授

报告时间：2025年6月11日14：00

报告地点：3B205

摘要：The classical Eulerian polynomials have two well-known combinatorial interpretations using

descent and exceedance of permutations. In this talk, we will define a multivariable generalization of the Eulerian polynomials using descent based and linear statistics of permutations and compute their generating function through a connection formula with another family of multivariable Eulerian polynomials enumerating exceedance and cyclic based statistics of permutations. As applications, we obtain the gamma-positivity of two generalized Eulerian polynomials with various interpretations of the gamma-coefficients. We also discuss a q-analogue related to the remixed Eulerian numbers. Our result generalizes and unifies several recent results in the literature.

专家简介：曾江，法国里昂第一大学教授，博士生导师，师从于组合数学国际权威 Dominique Foata教授。他曾是美国普林斯顿高等研究院的访问学者。主要研究组合数学、特殊函数、数论，在Journal of Combinaotrial Theory Series A, Advances in Applied Mathematics，Transactions of the American Mathematical Society，Proceedings of the London Mathematical Society，SIAM Journal on Discrete Mathematics，SIAM Journal on Mathematical Analysis，Journal of Number Theory等权威期刊发表学术论文100多篇，现任杂志 Seminaire Lotharingien de Combinatoire编委，Journal of Combinatorics and Number Theory的主编。