AI 中文总结
该研究确定了存在$n\boldsymbol{\u2265}3$个顶点的有限连通图$G$时，其对应的二项式边理想$J_G$的深度$t$与Krull维数$d$所满足的所有三元组$(n,t,d)$
AI 中文摘要
设$J_G$为多项式环$S$中有限图$G$的二项式边理想，确定所有满足$n\boldsymbol{\u2265}3$的三元组$(n,t,d)$，使得存在$n$个顶点的有限连通图$G$，满足${\rm depth}(S/J_G)=t$且$\text{dim}(S/J_G)=d$
英文摘要
Let $J_G$ denote the binomial edge ideal of a finite graph $G$ in the polynomial ring $S$. We determine all triples $(n,t,d)$ with $n\geq 3$ for which there exists a finite connected graph $G$ on $n$ vertices with ${\mathrm{depth}}(S/J_{G})=t$ and $\dim(S/J_G)=d$.
