Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-09T21:20:44.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Counting Partial Orders with a Fixed Number of Comparable Pairs

Published online by Cambridge University Press:  24 May 2001

HANS JÜRGEN PRÖMEL ,
ANGELIKA STEGER  and
ANUSCH TARAZ
HANS JÜRGEN PRÖMEL
Affiliation:
Institut für Informatik, Humboldt–Universität zu Berlin, 10099 Berlin, Germany (e-mail: proemel@informatik.hu-berlin.de, taraz@informatik.hu-berlin.de)
ANGELIKA STEGER
Affiliation:
Institut für Informatik, Technische Universität München, 80290 München, Germany (e-mail: steger@in.tum.de)
ANUSCH TARAZ
Affiliation:
Institut für Informatik, Humboldt–Universität zu Berlin, 10099 Berlin, Germany (e-mail: proemel@informatik.hu-berlin.de, taraz@informatik.hu-berlin.de)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In 1978, Dhar suggested a model of a lattice gas whose states are partial orders. In this context he raised the question of determining the number of partial orders with a fixed number of comparable pairs. Dhar conjectured that in order to find a good approximation to this number, it should suffice to enumerate families of layer posets. In this paper we prove this conjecture and thereby prepare the ground for a complete answer to the question.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 2 , March 2001 , pp. 159 - 177
Copyright
2001 Cambridge University Press