講座主題：Flow polynomials of a signed graph
專家姓名：錢建國
工作單位：廈門大學
講座時間：2018年10月15日14：30
講座地點：數(shù)學院小會議室
主辦單位：煙臺大學數(shù)學與信息科學學院
內(nèi)容摘要：
For a signed graphGand non-negative integerd, it was shown that there exists a polynomialFd(G,x) such that the number of the nowhere-zero Γ-flows inGequalsFd(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 inFd(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.
主講人介紹：
錢建國，廈門大學教授，博士生導師，美國數(shù)學會《數(shù)學評論》評論員，中國數(shù)學會組合數(shù)學與圖論學會理事，福建數(shù)學會理事，福建省組合數(shù)學與圖論學會常務(wù)理事。于1998年獲得四川大學理學博士學位，先后到德國Bielefeld大學和臺灣大學進行學術(shù)交流和訪問。在圖論組合領(lǐng)域頂級期刊《Journal of Combinatorial Theory, Series B》、《Journal of Combinatorial Theory, Series A》等雜志發(fā)表論文50余篇。主持和承擔多項國家自然科學基金和省自然科學基金項目，包括國家自然科學基金重點項目一項。
