講座主題：Flow polynomials of a signed graph
專家姓名：錢建國(guó)
工作單位：廈門大學(xué)
講座時(shí)間：2018年10月15日14：30
講座地點(diǎn)：數(shù)學(xué)院小會(huì)議室
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)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(guó)，廈門大學(xué)教授，博士生導(dǎo)師,，美國(guó)數(shù)學(xué)會(huì)《數(shù)學(xué)評(píng)論》評(píng)論員,，中國(guó)數(shù)學(xué)會(huì)組合數(shù)學(xué)與圖論學(xué)會(huì)理事，福建數(shù)學(xué)會(huì)理事,，福建省組合數(shù)學(xué)與圖論學(xué)會(huì)常務(wù)理事,。于1998年獲得四川大學(xué)理學(xué)博士學(xué)位，先后到德國(guó)Bielefeld大學(xué)和臺(tái)灣大學(xué)進(jìn)行學(xué)術(shù)交流和訪問(wèn),。在圖論組合領(lǐng)域頂級(jí)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(dān)多項(xiàng)國(guó)家自然科學(xué)基金和省自然科學(xué)基金項(xiàng)目,，包括國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目一項(xiàng),。
