主讲人：董峰明教授，新加坡南洋理工大学
报告时间：2019年12月23日15:30
报告地点：数计学院4号楼229
报告题目：New expressions for order polynomials and chromatic polynomials
报告摘要：In 1970, Stanley introduced the order polynomial and the strict order polynomial of a poset (i.e. partially ordered set). Let $P$ be a poset on $n$ elements with a binary relation $\preceq$. For $u,v\in P$, let $u\prec v$ mean that $u\preceq v$ but $u\ne v$. A mapping $\sigma: P\rightarrow [m]$ is said to be order-preserving (resp., strictly order-preserving) if $u\preceq v$ implies that $\sigma(u)\le \sigma(v)$ (resp., $u\prec v$ implies that $\sigma(u)< \sigma(v)$). let $\omega(p,x)$ (resp., $\bar\omega(p,x)$) be the function which counts the number of order-preserving (resp., strictly order-preserving) mappings $\sigma:p\rightarrow [m]$ whenever $x="m$" is a positive integer. both $\omega(p,x)$ and $\bar\omega(p,x)$ are polynomials in $x$ of degree $n$ and are respectively called the order polynomial and the strict order polynomial of $p$.
In this talk, I will introduce the order polynomial $\Omega(P,x)$ and its computations. I will also present our latest result on a new expression for $\Omega(P,x)$. By applying this new result and Stanley's work on the relation between order polynomials and chromatic polynomials $\chi(G,x)$ of graphs $G$, a new expression for $\chi(G,x)$ follows directly.
个人简介：董峰明，现为新加坡南洋理工大学副教授、博士生导师。1997年毕业于新加坡国立大学，获得博士学位；2008年，受邀访问英国剑桥大学牛顿数学科学研究所。主要研究兴趣为图论与拟阵论，特别是图和拟阵的结构与多项式的关系。出版专著《Chromatic polynomials and chromaticity of graphs》,已发表论文60余篇，解决了若干公开问题及猜想，包括Welsh和Bartel提出的“Shameful Conjecture”,是图的色多项式领域的著名专家。
