59 citations · 241 across the 37 of their papers we have counts for
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Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums
Catherine Greenhill, Brendan D. McKay
Let \svec = (s_1,...,s_m) and \tvec = (t_1,...,t_n) be vectors of nonnegative integer-valued functions of m,n with equal sum S = sum_{i=1}^m s_i = sum_{j=1}^n t_j. Let M(\svec,\tve…
The asymptotic volume of the Birkhoff polytope
E. Rodney Canfield, Brendan D. McKay
Let m,n be positive integers. Define T(m,n) to be the transportation polytope consisting of the m x n non-negative real matrices whose rows each sum to 1 and whose columns each sum…
Asymptotic enumeration of integer matrices with constant row and column sums
E. Rodney Canfield, Brendan D. McKay
Let s,t,m,n be positive integers such that sm=tn. Let M(m,s;n,t) be the number of m x n matrices over {0,1,2,...} with each row summing to s and each column summing to t. Equivalen…
Random dense bipartite graphs and directed graphs with specified degrees
Catherine Greenhill, Brendan D. McKay
Let S and T be vectors of positive integers with the same sum. We study the uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in…