An inequality between depth and Stanley depth

2009/05/28 by Dorin Popescu, Popescu, Dorin · 1 citation
Computer Science · Mathematics · #13C14 #13F20 #13H10 #13P10 #Advanced Optimization Algorithms Research #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13C14 #msc:13F20 #msc:13H10 #msc:13P10

paper · pdf · doi:10.48550/arxiv.0905.4597

openalex publication_date 2009/05/28 · arxiv created 2010/06/08 · arxiv updated 2010/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Stanley's Conjecture holds for square free monomial ideals in five variables, that is the Stanley depth of a square free monomial ideal in five variables is greater or equal with its depth.

Citations

• Stanley Decompositions, Pretty Clean Filtrations and Reductions Modulo Regular Elements
• Stanley depth of monomial ideals in three variables
• Stanley decompositions and localization
• Criterions for Shellable Multicomplexes

Cited by

• Size and Stanley depth of monomial ideals

Related

• Stanley depth on five generated, squarefree, monomial ideals
• Depth of factors of square free monomial ideals
• Combinatorial Reductions for the Stanley Depth of I and S/I
• Depth of some square free monomial ideals
• Values and bounds of the Stanley depth