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Counting Partial Orders with a Fixed Number of Comparable Pairs
Published online by Cambridge University Press: 24 May 2001
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.
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- 2001 Cambridge University Press
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