A non-partitionable Cohen-Macaulay simplicial complex

2015/04/30 by Art M. Duval, Bennet Goeckner, Caroline J. Klivans +1 · 1 citation
Mathematics · #math.CO #math.AC #msc:05E45 #msc:13F55

paper · pdf · doi:10.1016/j.aim.2016.05.011

published as Adv. Math. 299 (2016) 381-395 · Final version. 13 pages, 2 figures

arxiv created 2016/06/07 · arxiv updated 2016/06/08

Abstract

A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. 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.

Cited by

• Betti Posets and the Stanley Depth

Related

• Stanley decompositions and partitionable simplicial complexes
• A balanced non-partitionable Cohen-Macaulay complex
• Partition and Cohen-Macaulay Extenders
• Skeletons of monomial ideals
• Cohen-Macaulay Properties of Square-Free Monomial Ideals