报告题目：On a conjecture concerning the shuffle-compatible permutation statistics

报告人：严慧芳教授

报告时间：2022/05/25 09:30-12:00

报告地点：腾讯会议 594-203-057

报告摘要：The notion of shuffle-compatible permutation statistics was implicit in Stanley's work on P-partitions and was first explicitly studied by Gessel and Zhuang. The aim of this paper is to prove that the triple ${\rm (udr, pk, des)}$ is shuffle-compatible as conjectured by Gessel and Zhuang, where ${\rm udr}$ denotes the number of up-down runs, ${\rm pk}$ denotes the peak number, and ${\rm des}$ denotes the descent number. This is accomplished by establishing an ${\rm (udr, pk, des)}$-preserving bijection in the spirit of Baker-Jarvis and Sagan's bijective proofs of shuffle-compatibility property of permutation statistics. As an application, our bijection also enables us to prove that the pair $({\rm cpk}, {\rm cdes})$ is cyclic shuffle-compatible, where ${\rm cpk}$ denotes the cyclic peak number and ${\rm cdes}$ denotes the cyclic descent number.

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，博士生导师。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., J. Algebraic 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。