Depth and Stanley depth of the facet ideals of some classes of simplicial complexes

Czechoslovak Mathematical Journal

Xiaoqi Wei, Yan Gu¹ 

关键词: monomial ideal;    facet ideal;    depth;    Stanley depth;   

DOI  :  10.21136/CMJ.2017.0172-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  Let $\Delta_{n,d}$ (resp. $\Delta_{n,d}'$) be the simplicial complex and the facet ideal $I_{n,d}=(x_1\cdots x_d,x_{d-k+1}\cdots x_{2d-k},\ldots,x_{n-d+1}\cdots x_n)$ (resp. $J_{n,d}=(x_1\cdots x_d,x_{d-k+1}\cdots x_{2d-k},\ldots,x_{n-2d+2k+1}\cdots x_{n-d+2k},x_{n-d+k+1}\cdots x_nx_1\cdots x_k)$). When $d\geq2k+1$, we give the exact formulas to compute the depth and Stanley depth of quotient rings $S/J_{n,d}$ and $S/I_{n,d}^t$ for all $t\geq1$. When $d=2k$, we compute the depth and Stanley depth of quotient rings $S/J_{n,d}$ and $S/I_{n,d}$, and give lower bounds for the depth and Stanley depth of quotient rings $S/I_{n,d}^t$ for all $t\geq1$.

【 授权许可】

Unknown