学术报告

题      目： Study on tiered trees

报  告  人：董峰明   教授  (邀请人：周波 )

                                     新加坡南洋理工大学

时      间：5月11日  08：30-09：30

地     点：数科院西楼二楼会议室

报告人简介:

       新加坡南洋理工大学教授、博士生导师。图论专家。

摘      要：

       A tiered graph $G=(V,E)$ with $m $ tiers is a simple graph with $V\subseteq  \brk{n}$  ($:=\{1,2,\dots,n\}$) and with a surjective map $t$ from $V$ to $\brk{m}$, called the tiering map of $G$, such that $t(v) >t(v')$ holds whenever if  $v>v'$ and $vv'\in E$. For any ordered partition $\p=(p_1,p_2,\dots,p_m)$ of $n$, let $\sett_{\p}$ denote the set of tiered trees $T$ with vertex set $\brk{n}$ and with a tiering map $t: \brk{n}\rightarrow \brk{m}$ such that $|t^{-1}(i)|=p_i$  for all $i\in \brk{m}$. Let $P_{\p}(q)=\sum_{T\in \sett_{\p}}q^{w(T)}$, where $w(T)$ is the weight of $T$. Dugan, Glennon, Gunnells and Steingr\'imsson [J. Combin. Theory, Ser. A 164 (2019), 24-49] asked for an elementary proof of the identity $P_{\p}(q)=P_{\pi(\p)}(q)$ for any permutation $\pi$ of $1,2,\dots,m$, where $\pi(\p)=(p_{\pi(1)},p_{\pi(2)},\dots,p_{\pi(m)})$. We will prove an extension of this identity by applying Tutte polynomials. It  is a  joint work with Prof. Huifang Yan.