Asymptotic enumeration of binary matrices with bounded row and column sums

Abstract

Let An be the set 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 |An| = 2 n2 -ρn+δ√n. nO(1), for a constant ρ ≈ 1.42515, and δ = δ(n) ≈ 1.46016 for even n and 0 otherwise. Copyright © by SIAM.