Squarefree monomial ideals with constant depth function
J\"urgen Herzog, Marius Vladoiu
TL;DR
This paper classifies certain squarefree monomial ideals, such as edge, matroidal, and facet ideals of pure simplicial forests, that maintain a constant depth function across all powers.
Contribution
It provides a classification of squarefree monomial ideals with constant depth functions, focusing on specific classes like edge, matroidal, and facet ideals of pure simplicial forests.
Findings
Classified edge ideals with constant depth functions
Identified matroidal ideals with this property
Characterized facet ideals of pure simplicial forests with constant depth
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.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation