(k\)-shellable simplicial complexes and graphs

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 co...

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Bibliographic Details
Published inarXiv.org
Main Author Rahmati-Asghar, Rahim
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.01.2017
Subjects
Graphs
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Summary: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.
ISSN:2331-8422