当前位置:首页 |  学术交流学术交流

新加坡南洋理工大学董峰明教授学术报告

信息来源: 暂无 发布日期: 2019-12-16 浏览次数:

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。