A balanced non-partitionable Cohen-Macaulay complex
Combinatorics
2017-11-16 v1 Commutative Algebra
Abstract
In a recent paper, Duval, Goeckner, Klivans and Martin disproved the longstanding conjecture by Stanley, that every Cohen-Macaulay simplicial complex is partitionable. We construct counterexamples to this conjecture that are even \emph{balanced}, i.e., their underlying graph has a minimal coloring. This answers a question by Duval et al. in the negative.
Cite
@article{arxiv.1711.05529,
title = {A balanced non-partitionable Cohen-Macaulay complex},
author = {Martina Juhnke-Kubitzke and Lorenzo Venturello},
journal= {arXiv preprint arXiv:1711.05529},
year = {2017}
}
Comments
11 pages, 3 figures