Stanley decompositions and partitionable simplicial complexes
Juergen Herzog, Ali Soleyman Jahan, Siamak Yassemi
TL;DR
This paper explores the relationship between Stanley decompositions and partitionable Cohen-Macaulay simplicial complexes, proving conjectures for specific classes of monomial ideals and highlighting their interconnectedness.
Contribution
It demonstrates that Stanley's conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay complexes and proves these for certain classes of monomial ideals.
Findings
Stanley's conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay complexes.
Proved these conjectures for Cohen-Macaulay monomial ideals of codimension 2.
Proved these conjectures for Gorenstein monomial ideals of codimension 3.
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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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis