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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)
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Abstract

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.

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

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