SIAM Journal on Discrete Mathematics, Volume 34, Issue 3, Page 1602-1608, January 2020.
We define and study the notion of a minimal Cohen--Macaulay simplicial complex. We prove that any Cohen--Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen--Macaulay. We show that many interesting examples of Cohen--Macaulay complexes in combinatorics are minimal, including Rudin's ball, Ziegler's ball, the dunce hat, and the nonpartitionable Cohen--Macaulay complex of Duval, Goeckner, Klivans, and Martin. We further provide various ways to construct such complexes.

中文翻译：

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最小科恩-麦克劳简单群

SIAM离散数学杂志，第34卷，第3期，第1602-1608页，2020年1月。
我们定义并研究了最小Cohen-Macaulay简单复形的概念。我们证明了我们所知的任何科恩-马考雷复合物都被炮轰到最小，而我们给出了使科恩-马考雷最小化的充分条件。我们展示了组合式Cohen-Macaulay络合物中许多有趣的例子极少，包括Rudin的球，Ziegler球，笨拙的帽子和Duval，Goeckner，Klivans和Martin不可分割的Cohen-Macaulay络合物。我们进一步提供了构建此类复合物的各种方法。