报告题目：New expressions for order polynomials and chromatic polynomials

报告人：董峰明教授

时间：2019年12月23日15:30

地点：数计学院4号楼229

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 $\\sigma: P\ightarrow [m]$ 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)

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. 

报告人简介：董峰明简介：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。