Squarefree monomial ideals with constant depth function

2012/09/26 by Jürgen Herzog, Herzog, Jürgen, Marius Vladoiu +2
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1209.5890

14 pages

arxiv created 2012/09/26 · openalex publication_date 2012/09/26 · arxiv updated 2012/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study squarefree monomial ideals which have constant depth functions. Edge ideals, matroidal ideals and facet ideals of pure simplicial forests connected in codimension one with this property are classified.

Citations

• Simplicial complexes with rigid depth

Related

• Depth of powers of squarefree monomial ideals
• The normalized depth function of squarefree powers
• Resolutions of square-free monomial ideals via facet ideals: a survey
• Squarefree monomial ideals with maximal depth
• Depth of some special monomial ideals