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Stanley decompositions and partitionable simplicial complexes

Juergen Herzog·Ali Soleyman Jahan·Siamak Yassemi
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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.

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Juergen Herzog, Ali Soleyman Jahan, Siamak Yassemi. 2007-01-16. Stanley decompositions and partitionable simplicial complexes. https://arxiv.org/abs/math/0612848

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