2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121942We 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 pagesCommutative Algebratext