Simplicial complexes with rigid depth

Abstract

We extend a result of Minh and Trung to get criteria for $\depth I=\depth\sqrt{I}$ where $I$ is an unmixed monomial ideal of the polynomial ring $S=K[x_1,...,x_n]$. As an application we characterize all the pure simplicial complexes $\Delta$ which have rigid depth, that is, which satisfy the condition that for every unmixed monomial ideal $I\subset S$ with $\sqrt{I}=I_{\Delta }$ one has $\depth(I)=\depth(I_Δ).$

References in corpus (2)

• Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
• Stanley depth and size of a monomial ideal

Cited by in corpus (1)

• Squarefree monomial ideals with constant depth function