Enumeration of Series-Parallel Posets According To Heights

Abstract

The paper gives a new aspect for constructing non-isomorphic n-element posets from smaller ones. This construction leads to enumerating the number of non-isomorphic n-element posets of height k, kn. General forms for the relations between the generating functions of two arguments, viz. the cardinality of a poset and its height, for non-isomorphic essentially series, essentially parallel and (+,)-irreducible posets are derived. These relations lead to the counting of series-parallel n-element posets of height k, kn.