References & Citations
Mathematics > Commutative Algebra
Title: Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients
(Submitted on 14 Feb 2021 (v1), last revised 14 May 2024 (this version, v5))
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.
Submission history
From: Mircea Cimpoeaş [view email][v1] Sun, 14 Feb 2021 17:02:55 GMT (9kb)
[v2] Mon, 9 Aug 2021 15:27:17 GMT (9kb)
[v3] Wed, 3 Jan 2024 17:34:00 GMT (11kb)
[v4] Fri, 16 Feb 2024 19:07:49 GMT (11kb)
[v5] Tue, 14 May 2024 17:43:29 GMT (11kb)
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