Stanley depth and size of a monomial ideal

2010/11/30 by Jürgen Herzog, Herzog, Jürgen, Dorin Popescu +3 · 1 citation
Computer Science · Mathematics · #13F55 #13P10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13C15 #Rings, Modules, and Algebras #Secondary 13F20

paper · pdf · doi:10.48550/arxiv.1011.6462

openalex publication_date 2010/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by 1 is a lower bound for its depth. We show that the size is also a lower bound for its Stanley depth. Applying Alexander duality we obtain upper bounds for the regularity and Stanley regularity of squarefree monomial ideals.

Citations

• Stanley conjecture on intersections of four monomial prime ideals

Cited by

• Simplicial complexes with rigid depth

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