Stanley decompositions and partitionable simplicial complexes

Abstract

We study Stanley decompositions and show that Stanley's conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

10 pages

References in corpus (1)

• Castelnuovo-Mumford regularity of products of ideals

Cited by in corpus (1)

• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four