Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness
Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness
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DOI：
10.1016/j.jcta.2011.01.011
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Masahiro Hachimori;K. Kashiwabara
中科院分区：
文献类型：
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作者：
Masahiro Hachimori;K. Kashiwabara
对于单纯复形的属性 P，如果 Γ 本身不满足 P，但其所有适当的限制满足 P，则单纯复形 Γ 是 P 的障碍。在本文中，我们确定了维度 ⩽2 的可壳性的所有障碍，完善了 Wachs 之前的工作。因此，我们得到可剥壳性、可分割性和顺序科恩-麦考利性的障碍集合对于维度 ⩽2 都是一致的。我们还表明，这三组障碍物在旗形复合体类别中是一致的。这些结果表明，遗传可脱壳性、遗传可分配性和遗传顺序科恩-麦考利性这三个属性对于这些类是等效的。
For a property P of simplicial complexes, a simplicial complex Γ is an obstruction to P if Γ itself does not satisfy P but all of its proper restrictions satisfy P. In this paper, we determine all obstructions to shellability of dimension ⩽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 ⩽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.