A non-partitionable Cohen-Macaulay simplicial complex
Combinatorics
2016-06-08 v3 Commutative Algebra
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.
Cite
@article{arxiv.1504.04279,
title = {A non-partitionable Cohen-Macaulay simplicial complex},
author = {Art M. Duval and Bennet Goeckner and Caroline J. Klivans and Jeremy L. Martin},
journal= {arXiv preprint arXiv:1504.04279},
year = {2016}
}
Comments
Final version. 13 pages, 2 figures