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arXiv · 1701.02868

$k$-shellable simplicial complexes and graphs

Rahim Rahmati-Asghar
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Abstract

In this paper we show that a $k$-shellable simplicial complex is the expansion of a shellable complex. We prove that the face ring of a pure $k$-shellable simplicial complex satisfies the Stanley conjecture. In this way, by applying expansion functor to the face ring of a given pure shellable complex, we construct a large class of rings satisfying the Stanley conjecture. Also, by presenting some characterizations of $k$-shellable graphs, we extend some results due to Castrill\'{o}n-Cruz, Cruz-Estrada and Van Tuyl-Villareal.

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Rahim Rahmati-Asghar. 2017-01-11. $k$-shellable simplicial complexes and graphs. https://arxiv.org/abs/1701.02868

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