In this paper we study shellable posets (partially ordered sets), that is, finite posets such that the simplicial complex of chains is shellable. It is shown that all admissible lattices (including all finite semimodular and supersolvable lattices) and all bounded locally semimodular finite posets are shellable. A technique for labeling the edges of the Hasse diagram of certain lattices, due to R. Stanley, is generalized to posets and shown to imply shellability, while Stanley's main theorem on… CONTINUE READING