Simplicial complexes which are minimal Cohen-Macaulay

Yanyan Wang; Tongsuo Wu

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arXiv · 2103.16078

Simplicial complexes which are minimal Cohen-Macaulay

Yanyan Wang·Tongsuo Wu

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Abstract

Let $\D$ be a $(d-1)$-dimensional pure $f$-simplicial complex over vertex set $[n]$. In this paper, it is proved that $n=2d$ holds true if $\D$ is minimal Cohen-Macaulay. It is also indicated that the recent work of \cite{Dao2020} implies that shellable condition on a pure simplicial complex $\D$ is identical with CM properties of a full series of subcomplexes of $\D$.

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Yanyan Wang, Tongsuo Wu. 2021-03-30. Simplicial complexes which are minimal Cohen-Macaulay. https://arxiv.org/abs/2103.16078

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