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Turkish Journal of Mathematics

Authors

GUANGJUN ZHU

DOI

10.3906/mat-1505-90

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.

First Page

816

Last Page

823

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Mathematics Commons

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