A non-partitionable Cohen–Macaulay simplicial complex

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]