A balanced non-partitionable Cohen-Macaulay complex

Lorenzo Venturello; Martina Juhnke-Kubitzke

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A balanced non-partitionable Cohen-Macaulay complex

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arxiv 1711.05529 v1 pith:NH5R5T6L submitted 2017-11-15 math.CO math.AC

Martina Juhnke-Kubitzke , Lorenzo Venturello This is my paper

classification math.COmath.AC

keywords balancedcohen-macaulaycomplexconjectureduvalanswerscoloringconstruct

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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.

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