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理学院“格致”讲坛学术报告(第六期)

作者:  来源:   时间:2020-11-03  点击:

报告题目: Inclusion-exclusion cancellation and application to graph polynomials

报 告 人: 钱建国 教授

报告时间:2020115日(周四)上午8:15-10:15

报告地点:理学院会议室3-201

报告人简介:

钱建国,厦门大学数学科学学院教授,博士生导师,主要从事图论应用(化学图论、网络拓扑结构设计与优化)及组合计数方面的研究。现任中国组合数学与图论专业委员会委员,中国运筹学会图论分会常务理事,福建省运筹学会副理事长。美国数学会《数学评论》评论员,发表评论40 余篇;主持和参加多项国家面上及重点基金项目; 在包括J. Combin. Theory Ser A, Ser B)及 J. Graph Theory等在内的国内外专业期刊上发表学术论文60余篇。

报告摘要:

     Whitney's broken cycle theorem gives a very nice `cancellation' to reduce some terms in the chromatic polynomial (represented in the form of inclusion-exclusion) such that the remaining terms cannot be cancellated out anymore and therefore, yield a combinatorial interpretation for the coefficients of the chromatic polynomial. So far, the known cancellations for the inclusion-exclusion formula strongly depend on the prescribed (linear or partial) ordering on the index set. We give a new cancellation method, which does not require any ordering on the index set. Our method extends all the ordering-basedmethods known in the literature and in general reduces more terms. As examples, we apply our method to some classic graph polynomials.

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