Art M. Duval ; Bennet Goeckner ; Caroline J. Klivans ; Jeremy Martin - 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) - https://doi.org/10.46298/dmtcs.6325
A non-partitionable Cohen–Macaulay simplicial complex

Authors: Art M. Duval 1; Bennet Goeckner 2; Caroline J. Klivans 3; Jeremy Martin 2

  • 1 University of Texas [El Paso]
  • 2 Department of Mathematics [Kansas]
  • 3 Department of Mathematics

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.

https://doi.org/10.46298/dmtcs.6325
Source: HAL:hal-02173381v1
Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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Source : ScholeXplorer IsRelatedTo DOI 10.1016/s0304-3975(99)00195-4
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