English

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

R2 v1 2026-06-22T22:46:42.272Z