The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the...The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) + 12[n/2].展开更多
The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, resp...The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.展开更多
给定Grassmann流形的两个Schubert链σ_a,σ_b,我们有乘积公式σ_a·σ_b=sum from 0 δ(a,b,c)σ_c。在文献[1]中作者利用酉群表示论中的Schur函数给出了计算δ(a,b,c)的公式。反之,给定σ_c,σ_b,我们可以问有哪些a,使σ_c在σ_a&...给定Grassmann流形的两个Schubert链σ_a,σ_b,我们有乘积公式σ_a·σ_b=sum from 0 δ(a,b,c)σ_c。在文献[1]中作者利用酉群表示论中的Schur函数给出了计算δ(a,b,c)的公式。反之,给定σ_c,σ_b,我们可以问有哪些a,使σ_c在σ_a·σ_b中以δ(a,b,c)为系数出现?本文在文献[1]的基础上,利用Schubert计算与Schur函数运算的相似性及群表示论中的Branching公式进一步研究这一问题。展开更多
基金This work is supported by the Key Project of the Education Department of Hunan Province of China (05A037)by Scientific Research Fund of Hunan Provincial Education Department (06C515).
文摘The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) + 12[n/2].
基金the National Natural Science Foundation of China under Grant No.10671073Scientific Study Foundation of the Talented People Gathered by Nantong University+2 种基金Science and Technology Commission of Shanghai Municipality under Grant No.07XD14011Shanghai Leading Academic Discipline Project under Grant No.B407Natural Science Foundation of Jiangsu's Universities under Grant No.07KJB110090
文摘The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, respectively.
文摘给定Grassmann流形的两个Schubert链σ_a,σ_b,我们有乘积公式σ_a·σ_b=sum from 0 δ(a,b,c)σ_c。在文献[1]中作者利用酉群表示论中的Schur函数给出了计算δ(a,b,c)的公式。反之,给定σ_c,σ_b,我们可以问有哪些a,使σ_c在σ_a·σ_b中以δ(a,b,c)为系数出现?本文在文献[1]的基础上,利用Schubert计算与Schur函数运算的相似性及群表示论中的Branching公式进一步研究这一问题。
