2017/11/15 by Juhnke-Kubitzke, Martina, Venturello, Lorenzo
#05E45 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.05529
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 balanced, i.e., their underlying graph has a minimal coloring. This answers a question by Duval et al. in the negative.