Depth of factors of square free monomial ideals

Abstract

Let $I$ be an ideal of a polynomial algebra over a field, generated by $r$ square free monomials of degree $d$. If $r$ is bigger (or equal, if $I$ is not principal) than the number of square free monomials of $I$ of degree $d+1$, then $\depth_SI= d$. Let $J⊊I$, $J\ne 0$ be generated by square free monomials of degree $\ge d+1$. If $r$ is bigger than the number of square free monomials of $I\setminus J$ of degree $d+1$, or more generally the Stanley depth of $I/J$ is $d$, then $\depth_SI/J= d$. In particular, Stanley's Conjecture holds in theses cases.

Cited by in corpus (4)

• Depth and minimal number of generators of square free monomial ideals
• Stanley depth on five generated, squarefree, monomial ideals
• Stanley depth and simplicial spanning trees
• Depth in a pathological case