Hereditary-shellable simplicial complexes
Hereditary-shellable simplicial complexes
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发表时间：
2014
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通讯作者：
Masahiro Hachimori
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作者：
Masahiro Hachimori
遗传可shell的简单复合体是这样的复合体，任何限制，包括它们自己，都是可shell的。矩阵复合体是可遗传壳化的简单复合体的例子。证明了二维遗传可壳简单配合物的纯2骨架是可扩展可壳的。这推广了Björner和Eriksson关于2维矩阵复合体是可扩展壳化的结论。另一方面，我们给出了一个不可顶点分解的二维遗传可壳简单复合体的例子。进一步，我们讨论了纯骨架的性质强障碍物的壳性作为我们的结果的应用。
Hereditary-shellable simplicial complexes are those such that any restrictions, including themselves, are shellable. Matroid complexes are examples of hereditary-shellable simplicial complexes. We show that the pure 2-skeletons of 2-dimensional hereditary-shellable simplicial complexes are extendably shellable. This generalizes the result of Björner and Eriksson that matroid complexes of dimension 2 are extendably shellable. On the other hand, we give an example of a 2-dimensional hereditary-shellable simplicial complex that is not vertex decomposable. Further, we discuss properties of pure skeletons of strong obstructions to shellability as an application of our result.