# ALGEBRAIC COMBINATORICS

A balanced non-partitionable Cohen–Macaulay complex
Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1149-1157.

In a recent article, 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 balanced, i.e. their underlying graph has a minimal coloring. This answers a question by Duval et al. in the negative.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.78
Classification: 05E45,  13F55
Keywords: simplicial complex, balancedness, Cohen–Macaulay, partitionability
@article{ALCO_2019__2_6_1149_0,
author = {Juhnke-Kubitzke, Martina and Venturello, Lorenzo},
title = {A balanced non-partitionable {Cohen{\textendash}Macaulay} complex},
journal = {Algebraic Combinatorics},
pages = {1149--1157},
publisher = {MathOA foundation},
volume = {2},
number = {6},
year = {2019},
doi = {10.5802/alco.78},
mrnumber = {4049841},
zbl = {1428.05334},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.78/}
}
Juhnke-Kubitzke, Martina; Venturello, Lorenzo. A balanced non-partitionable Cohen–Macaulay complex. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1149-1157. doi : 10.5802/alco.78. https://alco.centre-mersenne.org/articles/10.5802/alco.78/

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