可壳性、可分割性和顺序Cohen-Macaulayness的障碍
Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness
摘要：
对于单纯复形的性质$\cal P$，如果$Γ$本身不满足$\cal P$，但它的所有适当限制都满足$\cal P$，则单纯复形$Γ$是对$\cal P$的障碍。本文确定了维数$\le 2$的可壳性的所有障碍，改进了Wachs的工作.因此，我们得到的一组障碍，壳的可分割性和顺序Cohen-Macaulayness都符合尺寸$\le 2$。我们还表明，这三组障碍物相吻合的类旗复合体。这些结果表明，这三个性质，遗传壳性，遗传可分割性，遗传序列Cohen-Macaulayness是等价的这些类。
英文摘要：
For a property $\cal P$ of simplicial complexes, a simplicial complex $Γ$ is an obstruction to $\cal P$ if $Γ$ itself does not satisfy $\cal P$ but all of its proper restrictions satisfy $\cal P$. In this paper, we determine all obstructions to shellability of dimension $\le 2$, refining the previous work by Wachs. As a consequence we obtain that the set of obstructions to shellability, that to partitionability and that to sequential Cohen-Macaulayness all coincide for dimensions $\le 2$. We also show that these three sets of obstructions coincide in the class of flag complexes. These results show that the three properties, hereditary-shellability, hereditary-partitionability, and hereditary-sequential Cohen-Macaulayness are equivalent for these classes.
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