Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums

@article{Canfield2005AsymptoticEO,
title={Asymptotic Enumeration of Dense 0-1 Matrices with Equal Row Sums and Equal Column Sums},
author={E. Rodney Canfield and Brendan D. McKay},
journal={Electr. J. Comb.},
year={2005},
volume={12}
}

Let s, t,m, n be positive integers such that sm = tn. Let B(m, s;n, t) be the number of m×n matrices over {0, 1} with each row summing to s and each column summing to t. Equivalently, B(m, s;n, t) is the number of semiregular bipartite graphs with m vertices of degree s and n vertices of degree t. Define the density λ = s/n = t/m. The asymptotic value of B(m, s;n, t) has been much studied but the results are incomplete. McKay and Wang (2003) solved the sparse case λ(1−λ) = o((mn)−1/2) using… CONTINUE READING