A non-partitionable Cohen-Macaulay simplicial complex

Abstract

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.

Final version. 13 pages, 2 figures

References in corpus (2)

• Combinatorial 3-manifolds with 10 vertices
• Betti posets and the Stanley depth

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