Vol. 90, No. 2, 1980

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Asymptotic enumeration of partially ordered sets

Deepak Dhar

Vol. 90 (1980), No. 2, 299–305
Abstract

We define the entropy function S(ρ) = Limn−∞2n2 lnN(n,ρ), where N(n,ρ) is the number of distinct partial order relations which may be defined on a set of n elements such that a fraction ρ of the possible n(n 1)2 pairs are comparable. We derive upper bounds to S(ρ) to show that S(ρ) < (12)ln2 if ρ .699.

Mathematical Subject Classification 2000
Primary: 06A10, 06A10
Secondary: 05A15
Milestones
Received: 17 July 1979
Published: 1 October 1980
Authors
Deepak Dhar