【摘要】：本文主要考慮了共點(diǎn)的n-圈圖Gl1,l=2.…,ln所生成的單純復(fù)形△s(Gl1,l=2.…,ln)和它的的邊理想的一些代數(shù)性質(zhì).本文主要包含兩個(gè)部分：第一部分,對(duì)給定的n-圈圖Gl1,l2,…,ln,我們用破圈法求得它的生成樹(shù),進(jìn)而得到Gl1,l2.…,ln生成的單純復(fù)形△s(Gl1,l2.…,ln).接著,我們給出了△s(Gl1,l2n…,ln)的一些代數(shù)性質(zhì)和f-向量的計(jì)算公式.第二部分,我們考慮n-圈圖G(此時(shí)我們記Gl1,l2,…,ln為G)的邊理想I(G)的算術(shù)秩ara(I(G)).關(guān)于ara(I(G))的計(jì)算,我們對(duì)圈長(zhǎng)li進(jìn)行分類(lèi),即li≡0 mod 3,li≡1 mod 3或者li≡2 mod 3,得出了當(dāng)li≡0,2 mod 3時(shí),bight(I(G))=pdR(R/I(G))= ara(I(G)),當(dāng)li≡1 mod 3時(shí),ara(I(G))-bight(I(G))≤k2,其中k2為圈長(zhǎng)為模3余1的圈的個(gè)數(shù).
[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，

本文編號(hào)：2352384