An inequality between depth and Stanley depth

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.

References in corpus (5)

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

Cited by in corpus (19)

• Special Stanley Decompositions
• Stanley decompositions and localization
• Stanley conjecture on intersections of four monomial prime ideals
• Lexsegment ideals of Hilbert depth 1
• Stanley depth of powers of the path ideal
• Depth of some square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• Three generated, squarefree, monomial ideals
• Upper bounds for the Stanley depth
• Values and bounds of the Stanley depth
• Depth and Stanley Depth of the Canonical Form of a factor of monomial ideals
• Stanley Conjecture on intersection of three monomial primary ideals
• The behavior of Stanley depth under polarization
• Computing the Stanley depth
• On the Stanley depth of a special class of Borel type ideals
• Stanley depth of monomial ideals
• Graph and depth of a monomial squarefree ideal
• Size and Stanley depth of monomial ideals
• Several inequalities regarding sdepth