Duval, Art M. and Goeckner, Bennet and Klivans, Caroline J. and Martin, Jeremy - A non-partitionable Cohen–Macaulay simplicial complex

dmtcs:6325 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
A non-partitionable Cohen–Macaulay simplicial complex

Authors: Duval, Art M. and Goeckner, Bennet and Klivans, Caroline J. and Martin, Jeremy

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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Submitted on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]


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