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- W2012097676 abstract "Let $Jvarsubsetneq I$ be two monomial ideals of the polynomial ring $S=mathbb{K}[x_1,ldots,x_n]$. In this paper, we provide two lower bounds for the Stanley depth of $I/J$. On the one hand, we introduce the notion of lcm number of $I/J$, denoted by $l(I/J)$, and prove that the inequality ${rm sdepth}(I/J)geq n-l(I/J)+1$ hold. On the other hand, we show that ${sdepth}(I/J)geq n-dim L_{I/J}$, where $dim L_{I/J}$ denotes the order dimension of the lcm lattice of $I/J$. We show that $I$ and $S/I$ satisfy Stanley's conjecture, if either the lcm number of $I$ or the order dimension of the lcm lattice of $I$ is small enough. Among other results, we also prove that the Stanley--Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture." @default.
- W2012097676 created "2016-06-24" @default.
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- W2012097676 date "2014-05-21" @default.
- W2012097676 modified "2023-09-27" @default.
- W2012097676 title "Two lower bounds for the Stanley depth of monomial ideals" @default.
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