Illinois Journal of Mathematics

Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals

S. A. Seyed Fakhari

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Let $I$ be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring $S$. In this paper, we provide a lower bound for the Stanley depth of $I$ and $S/I$. In particular, we prove that if $I$ is a squarefree monomial ideal which is generated in a single degree, then $\operatorname{sdepth} (I)\geq n-\ell(I)+1$ and $\operatorname{sdepth} (S/I)\geq n-\ell(I)$, where $\ell(I)$ denotes the analytic spread of $I$. This proves a conjecture of the author in a special case.

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Illinois J. Math., Volume 57, Number 3 (2013), 871-881.

First available in Project Euclid: 3 November 2014

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Zentralblatt MATH identifier

Primary: 13C15: Dimension theory, depth, related rings (catenary, etc.) 05E99: None of the above, but in this section
Secondary: 13C13: Other special types


Seyed Fakhari, S. A. Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals. Illinois J. Math. 57 (2013), no. 3, 871--881. doi:10.1215/ijm/1415023515.

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