论文标题
卡梅伦的同源不变 - walker图
Homological invariants of Cameron--Walker graphs
论文作者
论文摘要
令$ g $为$ [n] $和$ r = k [x_1，\ ldots，x_n] $的有限简单连接图，$ n $变量在字段$ k $上。 $ g $的边缘理想是$ r $的理想$ i（g）$，它是由$ \ {i，j \} $的$ x_ix_j $生成的，是$ g $的边缘。在本文中，可能的元组$（n，{\ rm depth}（r/i（g）），{\ rm reg}（r/i（g）），\ dim r/i（g），{\ rm deg} \ h（r/i（g）） $ h $ - $ r/i（g）$的$ h $ polynomial将完全确定$ [n] $的walker图。
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.
