Asymptotic enumeration of binary matrices with bounded row and column weights

Abstract

Consider the set A n of all n × n binary matrices in which the number of 1's in each row and column is at most n/2. We show that the redundancy, n 2 - log 2 |A n|, of this set equals ρn - δ√n + O(logn), for a constant ρ ≈ 1.42515, and δ = δ(n) ≈ 1.46016 for even n and 0 otherwise. © Copyright 2011 Hewlett-Packard Development Company, L.P.