报 告 人：林志聪（山东大学、教授、博士生导师）
报告时间：2022年7月20日上午10点
报告地点：理学院（陈章辉楼）442学术报告厅
联 系 人：晏卫根
欢迎广大师生参加！
报告摘要：
By considering the parity of the degrees and levels of nodes in increasing trees, a new combinatorial interpretation for the coefficients of the Taylor expansions of the Jacobi elliptic functions is found. As one application of this new interpretation, a conjecture of Ma--Mansour--Wang--Yeh is solved. Unifying the concepts of increasing trees and plane trees, Lin--Ma--Ma--Zhou introduced weakly increasing trees on a multiset. A symmetry joint distribution of ``even-degree nodes on odd levels'' and ``odd-degree nodes'' on weakly increasing trees is found, extending the Schett polynomials, a generalization of the Jacobi elliptic functions introduced by Schett, to multisets. A combinatorial proof and an algebraic proof of this symmetry are provided, as well as several relevant interesting consequences. Moreover, via introducing a group action on trees, we prove the partial $\gamma$-positivity of the multiset Schett polynomials, a result implies both the symmetry and the unimodality of these polynomials.
报告人简介：
林志聪，现为山东大学数学与交叉科学研究中心教授，博士生导师。主要从事计数组合学的研究，在《J. Combin. Theory Ser. A》、《Combinatorica》、《European J. Combin.》、《Proc. Amer. Math. Soc.》等多个学术刊物发表SCI学术论文30余篇。近期的研究兴趣主要集中在排列统计量及其相关组合结构上的双射和同分布问题。
