共点的n-圈图生成的单纯复形的f-向量和它的边理想的算术秩的计算

发布时间：2018-11-23 18:37

【摘要】：本文主要考虑了共点的n-圈图Gl1,l=2.…,ln所生成的单纯复形△s(Gl1,l=2.…,ln)和它的的边理想的一些代数性质.本文主要包含两个部分：第一部分,对给定的n-圈图Gl1,l2,…,ln,我们用破圈法求得它的生成树,进而得到Gl1,l2.…,ln生成的单纯复形△s(Gl1,l2.…,ln).接着,我们给出了△s(Gl1,l2n…,ln)的一些代数性质和f-向量的计算公式.第二部分,我们考虑n-圈图G(此时我们记Gl1,l2,…,ln为G)的边理想I(G)的算术秩ara(I(G)).关于ara(I(G))的计算,我们对圈长li进行分类,即li≡0 mod 3,li≡1 mod 3或者li≡2 mod 3,得出了当li≡0,2 mod 3时,bight(I(G))=pdR(R/I(G))= ara(I(G)),当li≡1 mod 3时,ara(I(G))-bight(I(G))≤k2,其中k2为圈长为模3余1的圈的个数.
[Abstract]:In this paper, we mainly consider the n-cycle graph Gl1,l=2.. , the simplex complex s (Gl1,l=2.) generated by ln. , ln) and some algebraic properties of its edge ideals. This article mainly includes two parts: the first part, for a given n-cycle graph Gl1,l2,. Ln, we use the method of breaking the loop to find its spanning tree, and then we get the Gl1,l2.. , ln generated simplex s (Gl1,l2.. , ln). Then we give us s (Gl1,l2n. Some algebraic properties of, ln) and the formula for calculating f-vector. In the second part, we consider the n-cycle graph G (in which case we note Gl1,l2,. The arithmetic rank ara (I (G). Of the edge ideal I (G) with ln being G) For the calculation of ara (I (G), we classify the cycle length li, that is, li 鈮，

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