Height counting of unlabeled interval and N-free posets

Abstract

This paper enumerates according to height the classes of unlabeled N-free posets, interval orders, and posets that are both N-free and interval orders. The last two classes are enumerated according to height in terms of generating functions. We apply an algorithmic method for height counting of connected N-free posets. Numerical results for n-element posets of height k, 1≤k≤n≤14, are included. © 2003 Elsevier B.V. All rights reserved.