Czechoslovak Mathematical Journal | |
Depth and Stanley depth of the facet ideals of some classes of simplicial complexes | |
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
【 预 览 】
Files | Size | Format | View |
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RO201910181782613ZK.pdf | 178KB | download |