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学术报告:Tutte polynomials and proper Tutte-mappings

发布时间:2017年04月18日 浏览次数:发布者:mathky

报告人:叶永南教授,

         台湾中央研究院数学所

报告题目:Tutte polynomials and proper Tutte-mappings

报告时间:2017年04月20日15:00

报告地点:海韵实验楼105

报告摘要:let G be a finite and connected graph with edge set E(G). Let σ be a sequence on the edge set of G and T be a spanning tree of G. We introduce the conceptions of σ-cut tail and σ-cycle tail of T, which are generalizations of the conceptions of internally and externally activities defined by Tutte, respectively. Furthermore, we give the definitions of proper Tutte mappings and deletion-contraction mappings. Using the deletion-contraction recursion which Tutte polynomials satisfy, we can construct deletion-contraction mappings. It is proven that deletion-contraction mappings are proper Tutte mappings. We give a characterization for deletion-contraction mappings. These results reveal the essence of deletion-contraction recursion of Tutte polynomials. With the benifit of deletion-contraction mappings, we consider G-parking functions and study a family of bijections between the set of G-parking functions and the set of spanning trees of G. In these bijections, we can naturally express the Tutte polynomial for a general connected graph G in terms of statistics of G-parking functions and read the parameters of G-parking functions on the corresponding spanning trees.

报告人简介:台北中研院数学所研究员, 1985年在美国纽约州立大学获博士学位。1987年返台担任中央研究院数学所副研究员。1991年1月晋升为研究员迄今。 曾任加拿大魁北克大学资讯与数学系研究学者,麻省理工学院数学系、柏克莱加州大学统计系和澳洲Monash大学经济系访问学者。 学术研究除了数学之外, 还涉及物理化学、统计、经济等多个领域, 曾任台北数学推动中心主任, 中研院数学所副所长, 多次获得台湾杰出研究奖, 杰出研究计划奖。 组合论国际顶级杂志JCTA曾出版专门文章介绍Yeh-species, 这个由叶永南研究员名字命名的领域, 现在这一方向的研究仍然在不断深入。目前, 叶永南研究员的研究主要在图的Tutte多项式及其相关组合结构和计算组合uniform partitions方面。

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