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A non-partitionable Cohen–Macaulay simplicial complex
1 : University of Texas [El Paso]
(UTEP)
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Website
500 W University Ave, El Paso, TX 79968, États-Unis -
États-Unis
2 : Department of Mathematics [Kansas]
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Website
Department of Mathematics Kansas State University Manhattan -
États-Unis
3 : Department of Mathematics
Brown University 151 Thayer Street Providence, RI 02912 USA -
États-Unis
A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. 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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