Stanley Conjecture in small embedding dimension

Abstract

We show that Stanley's conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.

5 pages

References in corpus (3)

• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four
• Criterions for Shellable Multicomplexes
• Stanley decompositions and partitionable simplicial complexes

Cited by in corpus (20)

• Stanley depth of complete intersection monomial ideals
• An inequality between depth and Stanley depth
• Stanley depth of monomial ideals with small number of generators
• Stanley decompositions and localization
• Stanley depth of monomial ideals in three variables
• Stanley depth of powers of the path ideal
• Stanley decompositions of squarefree modules and Alexander duality
• On the Behaviour of Stanley Depth under Variable Adjunction
• Stanley Depth of Multigraded Modules
• On a conjecture of Stanley depth of squarefree Veronese ideals
• A note on Stanley conjecture for monomial ideals
• Upper bounds for the Stanley depth
• Stanley depth of edge ideals
• The behavior of Stanley depth under polarization
• An algorithm for computing the multigraded Hilbert depth of a module
• Computing the Stanley depth
• On the Stanley depth of edge ideals of k-partite clutters
• Stanley Decompositions and Polarization
• Hilbert series and Hilbert depth of squarefree Veronese ideals
• Depth and Stanley depth of multigraded modules