Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph

Authors

GUANGJUN ZHU

DOI

10.3906/mat-1603-114

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

First Page

1174

Last Page

1183

Recommended Citation

ZHU, GUANGJUN (2017) "Depth and Stanley depth of the path ideal associated to an $n$-cyclic graph," Turkish Journal of Mathematics: Vol. 41: No. 5, Article 9. https://doi.org/10.3906/mat-1603-114
Available at: https://journals.tubitak.gov.tr/math/vol41/iss5/9