- Turkish Journal of Mathematics
- Vol: 40 Issue: 4
- A lower bound for Stanley depth of squarefree monomial ideals
A lower bound for Stanley depth of squarefree monomial ideals
Authors : Guangjun Zhu
Pages : 816-823
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Stanley depth, Stanley conjecture, monomial ideal, Schmitt--Vogel number, $n$-cyclic graph