Depth and minimal number of generators of square free monomial ideals

Abstract

Let $I$ be an ideal of a polynomial algebra $S$ over a field generated by square free monomials of degree $\ge d$. 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.

References in corpus (4)

• An inequality between depth and Stanley depth
• Special Stanley Decompositions
• Stanley conjecture on intersections of four monomial prime ideals
• Depth of factors of square free monomial ideals

Cited by in corpus (3)

• Depth of some square free monomial ideals
• Three generated, squarefree, monomial ideals
• Depth of some special monomial ideals