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arXiv · 1702.00781

Combinatorial Reductions for the Stanley Depth of $I$ and $S/I$

Mitchel T. Keller·Stephen J. Young
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Abstract

We develop combinatorial tools to study the relationship between the Stanley depth of a monomial ideal $I$ and the Stanley depth of its compliment, $S/I$. Using these results we are able to prove that if $S$ is a polynomial ring with at most 5 indeterminates and $I$ is a square-free monomial ideal, then the Stanley depth of $S/I$ is strictly larger than the Stanley depth of $I$. Using a computer search, we are able to extend this strict inequality up to polynomial rings with at most 7 indeterminates. This partially answers questions asked by Propescu and Qureshi as well as Herzog.

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Mitchel T. Keller, Stephen J. Young. 2017-02-02. Combinatorial Reductions for the Stanley Depth of $I$ and $S/I$. https://arxiv.org/abs/1702.00781

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