A note on Stanley conjecture for monomial ideals

Abstract

In this paper, we prove that if $I\subset S:=K[x_1,...,x_n]$ is a monomial ideal then $I$ and $S/I$ satisfy the Stanley conjecture when $I$ has a small number of generators, with respect to $\depth(S/I)$ and $\max\{|P|:\;P\in\Ass(S/I)\}$. In particular, if $I$ be a monomial almost complete intersection ideal in $S$, then Stanley's Conjecture holds for $S/I$ and $I$.

This paper was withdrawn because it was accepted to be published in Bull. Math. Soc. Roumanie with the title changed in "The Stanley conjecture on monomial almost complete intersection ideals". One can find the new version of the paper on Arxiv:1112.4956

References in corpus (4)

• Stanley Conjecture in small embedding dimension
• Stanley Decompositions, Pretty Clean Filtrations and Reductions Modulo Regular Elements
• Stanley decompositions and localization
• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Cited by in corpus (2)

• On the Stanley Depth of Squarefree Veronese Ideals
• On a conjecture of Stanley depth of squarefree Veronese ideals