A non-partitionable Cohen–Macaulay simplicial complex

Art M. Duval; Bennet Goeckner; Caroline J. Klivans; Jeremy Martin

doi:10.46298/dmtcs.6325

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 complexArticle

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]

Bibliographic References

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