Simplicial complexes with rigid depth

2012/01/16 by Adnan Aslam, Aslam, Adnan, Viviana Ene +1
Computer Science · Mathematics · #13C15 #13D45 #13F55 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1201.3325

openalex publication_date 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a result of Minh and Trung to get criteria for \depth I=\depth√(I) where I is an unmixed monomial ideal of the polynomial ring S=K[x₁,..., x_n]. As an application we characterize all the pure simplicial complexes Δ which have rigid depth, that is, which satisfy the condition that for every unmixed monomial ideal I⊂ S with √(I)=I_Δ one has \depth(I)=\depth(I_Δ).

Citations

• Stanley depth and size of a monomial ideal

Related

• Depth and Stanley depth of the facet ideal associated to a line-type simplicial complex
• The facet ideal of a simplicial complex
• Graph and depth of a monomial squarefree ideal
• Depth of an initial ideal
• Depth of some special monomial ideals