Turkish Journal of Mathematics
Abstract
Let $S=K[x_{1},\dots,x_{n}]$ be a polynomial ring over a field $K$ in $n$ variables and $I$ a squarefree monomial ideal of $S$ with Schmitt--Vogel number $sv(I)$. In this paper, we show that $\mbox{sdepth}\,(I)\geq \mbox{max}\,\{1, n-1-\lfloor \frac{sv(I)}{2}\rfloor\},$ which improves the lower bound obtained by Herzog, Vladoiu, and Zheng. As some applications, we show that Stanley's conjecture holds for the edge ideals of some special $n$-cyclic graphs with a common edge.
DOI
10.3906/mat-1505-90
Keywords
Stanley depth, Stanley conjecture, monomial ideal, Schmitt--Vogel number, $n$-cyclic graph
First Page
816
Last Page
823
Recommended Citation
ZHU, GUANGJUN
(2016)
"A lower bound for Stanley depth of squarefree monomial ideals,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 10.
https://doi.org/10.3906/mat-1505-90
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/10
