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: 10.5802/alco.78
Keywords: simplicial complex, balancedness, Cohen–Macaulay, partitionability
Juhnke-Kubitzke, Martina 1; Venturello, Lorenzo 1
@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}, zbl = {1428.05334}, mrnumber = {4049841}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.78/} }
TY - JOUR AU - Juhnke-Kubitzke, Martina AU - Venturello, Lorenzo TI - A balanced non-partitionable Cohen–Macaulay complex JO - Algebraic Combinatorics PY - 2019 SP - 1149 EP - 1157 VL - 2 IS - 6 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.78/ DO - 10.5802/alco.78 LA - en ID - ALCO_2019__2_6_1149_0 ER -
%0 Journal Article %A Juhnke-Kubitzke, Martina %A Venturello, Lorenzo %T A balanced non-partitionable Cohen–Macaulay complex %J Algebraic Combinatorics %D 2019 %P 1149-1157 %V 2 %N 6 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.78/ %R 10.5802/alco.78 %G en %F ALCO_2019__2_6_1149_0
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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