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

Wei, Xiaoqi, and Gu, Yan. "Depth and Stanley depth of the facet ideals of some classes of simplicial complexes." Czechoslovak Mathematical Journal 67.3 (2017): 753-766. <http://eudml.org/doc/294092>.

@article{Wei2017,
abstract = {Let $\Delta _\{n,d\}$ (resp. $\Delta _\{n,d\}^\{\prime \}$) 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. $J_\{n,d\}=(x_\{1\}\cdots x_\{d\},x_\{d-k+1\}\cdots x_\{2d-k\},\ldots ,x_\{n-2d+2k+1\}\cdots x_\{n-d+2k\},x_\{n-d+k+1\}\cdots x_\{n\}x_\{1\}\cdots x_\{k\})$). When $d\ge 2k+1$, 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 $t\ge 1$. 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 $t\ge 1$.},
author = {Wei, Xiaoqi, Gu, Yan},
journal = {Czechoslovak Mathematical Journal},
keywords = {monomial ideal; facet ideal; depth; Stanley depth},
language = {eng},
number = {3},
pages = {753-766},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Depth and Stanley depth of the facet ideals of some classes of simplicial complexes},
url = {http://eudml.org/doc/294092},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Wei, Xiaoqi
AU - Gu, Yan
TI - Depth and Stanley depth of the facet ideals of some classes of simplicial complexes
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 753
EP - 766
AB - Let $\Delta _{n,d}$ (resp. $\Delta _{n,d}^{\prime }$) 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. $J_{n,d}=(x_{1}\cdots x_{d},x_{d-k+1}\cdots x_{2d-k},\ldots ,x_{n-2d+2k+1}\cdots x_{n-d+2k},x_{n-d+k+1}\cdots x_{n}x_{1}\cdots x_{k})$). When $d\ge 2k+1$, 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 $t\ge 1$. 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 $t\ge 1$.
LA - eng
KW - monomial ideal; facet ideal; depth; Stanley depth
UR - http://eudml.org/doc/294092
ER -