A non-partitionable Cohen–Macaulay simplicial complex

Art M. Duval (1) , Bennet Goeckner (2) , Caroline J. Klivans (3) , Jeremy Martin (2)

1 UTEP - 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.

Domaines: Combinatoire [math.CO]

Art M. Duval, Bennet Goeckner, Caroline J. Klivans, Jeremy Martin. A non-partitionable Cohen–Macaulay simplicial complex. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6325⟩. ⟨hal-02173381⟩