  Let S=(s_1,s_2,..., s_m) and T = (t_1,t_2,..., t_n) be vectors of
non-negative integers with sum_{i=1}^{m} s_i = sum_{j=1}^n t_j. Let B(S,T) be
the number of m*n matrices over {0,1} with j-th row sum equal to s_j for 1 <= j
<= m and k-th column sum equal to t_k for 1 <= k <= n. Equivalently, B(S,T) is
the number of bipartite graphs with m vertices in one part with degrees given
by S, and n vertices in the other part with degrees given by T. Most research
on the asymptotics of B(S,T) has focused on the sparse case, where the best
result is that of Greenhill, McKay and Wang (2006). In the case of dense
matrices, the only precise result is for the case of equal row sums and equal
column sums (Canfield and McKay, 2005). This paper extends the analytic methods
used by the latter paper to the case where the row and column sums can vary
within certain limits. Interestingly, the result can be expressed by the same
formula which holds in the sparse case.
