Cameron-Walker图的同调不变量
Homological invariants of Cameron--Walker graphs
摘要：
设$G$是$[n]$上的有限简单连通图，$R = K[x_1, \ldots, x_n]$是域$K$上的以$n$为变量的多项式环. $G$的边理想是$R$的理想$I(G)$，它是由那些单项式$x_ix_j$生成的，对于这些单项式$x_ix_j$，$\{i, j\}$是$G$的边。本文将完全确定$[n]$上的Cameron-Walker图所产生的可能元组$(n, {\rm depth} (R/I(G)), {\rm reg} (R/I(G)), \dim R/I(G), {\rm deg} \ h(R/I(G)))$，其中${\rm deg} \ h(R/I(G))$是$R/I(G)$的$h$ -多项式的次数.
英文摘要：
Let $G$ be a finite simple connected graph on $[n]$ and $R = K[x_1, \ldots, x_n]$ the polynomial ring in $n$ variables over a field $K$. The edge ideal of $G$ is the ideal $I(G)$ of $R$ which is generated by those monomials $x_ix_j$ for which $\{i, j\}$ is an edge of $G$. In the present paper, the possible tuples $(n, {\rm depth} (R/I(G)), {\rm reg} (R/I(G)), \dim R/I(G), {\rm deg} \ h(R/I(G)))$, where ${\rm deg} \ h(R/I(G))$ is the degree of the $h$-polynomial of $R/I(G)$, arising from Cameron--Walker graphs on $[n]$ will be completely determined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
