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 an 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 Castrillon-Cruz, Cruz-Estrada and Van Tuyl-Villareal.