A non-partitionable Cohen-Macaulay simplicial complex
نویسندگان
چکیده
A long-standing conjecture of Stanley states that every Cohen– Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves the conjecture that the Stanley depth of a monomial ideal is always at least its depth.
منابع مشابه
Stanley Decompositions and Partitionable Simplicial Complexes
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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