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arXiv · 2102.07196

Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients

Andreea I. Bordianu·Mircea Cimpoeas
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Abstract

We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and $\operatorname{depth}(S/I)=n-2$, then $\operatorname{sdepth}(S/I)=n-2$ and, if $I$ is squarefree, $\operatorname{hdepth}(S/I)=n-2$. Also, we prove that $\operatorname{sdepth}(S/I)\geq \operatorname{depth}(S/I)$ for a monomial ideal $I$ with linear quotients which satisfies certain technical conditions.

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Andreea I. Bordianu, Mircea Cimpoeas. 2021-02-14. Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients. https://arxiv.org/abs/2102.07196

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