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A Non-Partitionable Cohen-Macaulay Simplicial Complex
Duval, Art M. Goeckner, Bennet Klivans, Caroline J. Martin, Jeremy L.
Duval, Art M.
Goeckner, Bennet
Klivans, Caroline J.
Martin, Jeremy L.
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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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Date
2016-08-20
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Elsevier
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Keywords
Simplicial complex, H-vector;, Cohen–Macaulay, Constructibility, Partitionability, Stanley depth
Citation
Art M. Duval, Bennet Goeckner, Caroline J. Klivans and Jeremy L. Martin. A non-partitionable Cohen-Macaulay simplicial complex. Advances in Mathematics 299 (2016), 381-395.