- Turkish Journal of Mathematics
- Vol: 41 Issue: 5
- Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph
Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph
Authors : Guangjun Zhu
Pages : 1174-1183
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We compute the depth and Stanley depth for the quotient ringof the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for the depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1\,(\mbox{mod}\ 4)$,and for Stanley depth when $n\equiv 0,3\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1,2\,(\mbox{mod}\ 4)$. We also give some formulas forthe depth and Stanley depth of a quotient of the path ideals of length $n-1$ and $n$.Keywords : Stanley depth, Stanley inequality, path ideal, cyclic graph