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

报告时间:2020年11月3日下午15:00

报告地点：科学会堂A710报告厅

报告人：

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-based”methods known in the literature and in general reduces more terms. As examples, we apply our method to some classic graph polynomials.