Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2003-19

November 2003

The Number of Linear Extensions of the Boolean Lattice

Graham Brightwell and Prasad Tetali

Abstract

Let L(Q^t) denote the number of linear extensions of the t-dimensional Boolean lattice Q^t. We use the entropy method of Kahn to show that

$\begin{displaymath} \frac{\log(L(Q^t))}{2^t} = \log{t \choose \lfloor{t/2}\rfloor} - \frac{3}{2}\log e + o(1), \end{displaymath}$

where the logarithms are base 2. We also find the exact maximum number of linear extensions of a d-regular bipartite order on n elements, in the case when n is a multiple of 2d.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7732. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk