主 讲 人 ：潘琼琼    副教授

活动时间：2025-12-08 09:00:00

地      点 ：腾讯会议：723-722-909

主办单位：数学科学学院

讲座内容：

The generating polynomial of all $n$--permutations with respect to the number of alternating runs possesses a root at $-1$ of multiplicity $\lfloor (n-2)/2\rfloor$ for$n\ge2$.

This fact can be deduced by combining the David--Barton formula for Eulerian polynomials with the Foata--Schützenberger $\gamma$--decomposition of these polynomials. Recently, Bóna provided a group--action proof of this result. In this talk, I propose an alternative approach based on the Hetyei--Reiner action on binary trees, which yields a new combinatorial interpretation of Bóna’s quotient polynomial. Furthermore, we extend our study to analogous results for permutations of types~B and~D. As a consequence of our bijective framework, we also obtain combinatorial proofs of David--Barton type identities for permutations of types~A and~B.

This talk is based on a joint work with Yunze Wang and Jiang Zeng.

主讲人介绍：

潘琼琼，2020年博士毕业于法国里昂大学，2021年入职温州大学，主要研究计数组合学以及正交多项式理论。多篇论文发表在JCTA、AAM、DM、EJC等组合数学领域国际期刊上，目前主持一项国家自然科学基金青年项目。