On Lexicographically Shellable Posets

Abstract

Lexicographically shellable partially ordered sets are studied.A new recursive formulation of CL-shellability is introduced and exploited.It is shown that face lattices of convex polytopes, totally semimodular posets, posets of injective and normal words and lattices of bilinear forms are CL-shellable.Finally, it is shown that several common operations on graded posets preserve shellability and CL-shellability.