讲座主题：Flow polynomials of a signed graph

专家姓名：钱建国

工作单位：厦门大学

讲座时间：2018年10月15日14：30

讲座地点：数学院小会议室

主办单位：hy590海洋之神平台数学与信息科学学院

内容摘要：

For a signed graphGand non-negative integerd, it was shown that there exists a polynomialF_d(G,x) such that the number of the nowhere-zero Γ-flows inGequalsF_d(G,x) evaluated atkfor every Abelian group Γ of orderkwith

, where (Γ) is the largest integerdfor which Γ has a subgroup isomorphic to

. We define a class of particular directed circuits inG, namely the fundamental directed circuits, and show that all Γ-flows (not necessarily nowhere-zero) inGcan be generated by these circuits. It turns out that all Γ-flows inGcan be evenly classified into 2^(Γ)-classes specified by the elements of order 2 in Γ, each class of which consists of the same number of flows depending only on the order of Γ. Using an extension of Whitney’s broken circuit theory we give a combinatorial interpretation of the coefficients inF_d(G,x) ford= 0, in terms of the broken bonds. Finally, we show that the sets of edges in a signed graph that contain no broken bond form a homogeneous simplicial complex.

主讲人介绍：

钱建国，厦门大学教授，博士生导师，美国数学会《数学评论》评论员，中国数学会组合数学与图论学会理事，福建数学会理事，福建省组合数学与图论学会常务理事。于1998年获得四川大学理学博士学位，先后到德国Bielefeld大学和台湾大学进行学术交流和访问。在图论组合领域顶级期刊《Journal of Combinatorial Theory, Series B》、《Journal of Combinatorial Theory, Series A》等杂志发表论文50余篇。主持和承担多项国家自然科学基金和省自然科学基金项目，包括国家自然科学基金重点项目一项。