In this paper we show that a $k$-shellable simplicial complex is theexpansion 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 shellablecomplex, we construct a large class of rings satisfying the Stanley conjecture. Also, by presenting some characterizations of $k$-shellable graphs, we extendsome results due to Castrill\'{o}n-Cruz, Cruz-Estrada and Van Tuyl-Villareal.
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机译：在本文中，我们证明了$ k $-可带壳的简单复形是可带壳的复形的扩展。我们证明了一个纯可带壳$ k $的简单复合体的面环满足Stanley猜想。这样，通过将膨胀函子应用于给定纯壳可配合物的面环，我们构造了满足Stanley猜想的一大类环。另外，通过介绍$ k $可壳图的一些特征，由于Castrill'n-Cruz，Cruz-Estrada和Van Tuyl-Villareal，我们扩展了一些结果。
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