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arXiv · 1504.04279

A non-partitionable Cohen-Macaulay simplicial complex

Art M. Duval·Bennet Goeckner·Caroline J. Klivans·Jeremy L. Martin
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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.

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Art M. Duval, Bennet Goeckner, Caroline J. Klivans, Jeremy L. Martin. 2016-06-07. A non-partitionable Cohen-Macaulay simplicial complex. https://doi.org/10.1016/j.aim.2016.05.011

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