报告题目：Statistics on Quasi-Stirling Permutations of Multisets and Partial -Positivity

报告人：严慧芳 教授（浙江师范大学）

报告时间：2021 年 9 月 17 日（星期五） 15:30-16:30

报告地点：腾讯会议 ID：151 110 599

校内联系人：陈曦 84708351-8025

报告摘要: A permutation  of a multiset is said to be a quasi-Stirling permutation if there does not exist four indices  such that  and . In this talk, we will present some recent results on the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents, which generalizes several results for quasi-Stirling permutations on  obtained by Elizalde and solve two open problems posed by Elizalde. Moreover, we prove that the enumerative polynomials are partial -positive, thereby confirming a recent conjecture posed by Lin, Ma and Zhang. This is accomplished by proving the partial -positivity of the enumerative polynomials of certain ordered labeled trees, which are in bijection with quasi-Stirling permutations of multisets.  As an application, we provide an alternative proof of the partial -positivity of the enumerative polynomials on Stirling permutations of multisets.

报告人简介：严慧芳，2006年博士毕业于南开大学组合数学研究中心，现任浙江师范大学数学与计算机科学学院教授，硕士生导师。主要研究组合结构的计数以及组合统计量方面的问题， 在J. Combin. Theory Ser. A， Adv in Appl. Math., European J. Combin.等杂志上发表论文30余篇。先后主持国家自然科学基金3项（面上2项， 青年1项）， 浙江省自然科学基金一项。