37000gcom威尼斯2023年第20期数理大讲堂

报告题目：More bijective combinatorics of weakly increasing trees

报告人：林志聪

报告时间：2023年5月27日 9:55-10:40

报告地点：37000gcom威尼斯3号楼3B205

摘要：

As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin--Ma--Ma--Zhou (2021). Various intriguing connections and bijections for weakly increasing trees have already been found and the purpose of this paper is to present yet more bijective combinatorics on this unified object. Two of our main contributions are

\begin{itemize}

\item extension of an equidistribution result on plane trees due to Eu--Seo--Shin (2017), regarding levels and degrees of nodes, to weakly increasing trees;

\item a new interpretation of the multiset Schett polynomials in terms of odd left/right chains on weakly increasing binary trees.

\end{itemize}

Interesting consequences are discussed, including new tree interpretations for the Jacobi elliptic functions and Euler numbers. Relevant enumerative results are also presented, involving recurrence relations, exponential generating functions and context-free grammars.

专家简介：

林志聪，山东大学数学与交叉科学研究中心教授、齐鲁青年学者，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.》等权威期刊发表SCI学术论文40余篇。任中国数学会计算机数学专业委员会委员。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。