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  1. Home > Articles & Issues >
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  3. A non-partitionable ...
Conference paper

A non-partitionable Cohen–Macaulay simplicial complex

Art M. Duval (1), Bennet Goeckner (2), Caroline J. Klivans (3) (4), Jeremy Martin (2)
(1) University of Texas [El Paso]
(2) Department of Mathematics [Kansas]
(3) Department of Mathematics
(4) Department of Mathematics [Providence]
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July 4, 2016
Published on
April 22, 2020
Last modified on
March 31, 2025
Volume
DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
DOI
10.46298/dmtcs.6325
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A non-partitionable Cohen–Macaulay simplicial complex

Art M. Duval (1), Bennet Goeckner (2), Caroline J. Klivans (3) (4), Jeremy Martin (2)
(1) University of Texas [El Paso]
(2) Department of Mathematics [Kansas]
(3) Department of Mathematics
(4) Department of Mathematics [Providence]
Abstract
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.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
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