标题： 常规边，匹配和Hilbert级数 显示英文标题

标题： Regular Edges, Matchings and Hilbert Series

摘要： 当$I$是图$G$的边理想时，我们利用组合性质，特别是关于边的邻居连通性的 Property$P$，来分类当顶点的二项式和在$R/I(G)$上是一个正则元素的情况。 在一种温和的可分离性假设下，我们确定这些元素何时可以组合成一个正则序列。 利用这些正则序列，我们证明了 Hilbert 系列和相应的$h$-向量可以通过对相关图进行简化计算来计算，该计算基于相关图的$f$-向量或独立向量。 在图是Cohen-Macaulay且具有满足分离性准则的正则边完美匹配的情况下，$h$-向量的$R/I(G)$将恰好是顶点数为$G$一半的图的Stanley-Reisner复形的$f$-向量。 显示英文摘要

摘要： When $I$ is the edge ideal of a graph $G$, we use combinatorial properities, particularly Property $P$ on connectivity of neighbors of an edge, to classify when a binomial sum of vertices is a regular element on $R/I(G)$. Under a mild separability assumption, we identify when such elements can be combined to form a regular sequence. Using these regular sequences, we show that the Hilbert series and corresponding $h$-vector can be calculated from a related graph using a simplified calculation on the $f$-vector, or independence vector, of the related graph. In the case when the graph is Cohen-Macaulay with a perfect matching of regular edges satisfying the separability criterion, the $h$-vector of $R/I(G)$ will be precisely the $f$-vector of the Stanley-Reisner complex of a graph with half as many vertices as $G$.