Asymptotic enumeration of partially ordered sets

Dhar, Deepak (1980) Asymptotic enumeration of partially ordered sets Pacific Journal of Mathematics, 90 (2). pp. 299-305. ISSN 0030-8730

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The author define the entropy function S( ρ)=Limn- ∞ 2n−2lnN (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)<(l/2) In 2 if ρ>.699.

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Deposited On:10 Feb 2012 04:13
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