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arXiv · 1107.2621

Depth and minimal number of generators of square free monomial ideals

Dorin Popescu
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Abstract

Let $I$ be an ideal of a polynomial algebra $S$ over a field generated by square free monomials of degree $\geq d$. If $I$ contains more monomials of degree $d$ than $(n-d)/(n-d+1)$ of the total number of square free monomials of $S$ of degree $d+1$ then $\depth_SI\leq d$, in particular the Stanley's Conjecture holds in this case.

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Dorin Popescu. 2011-10-14. Depth and minimal number of generators of square free monomial ideals. https://arxiv.org/abs/1107.2621

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