Let s, t,m, n be positive integers such that sm = tn. Let M(m, s;n, t) be the number of m × n matrices over {0, 1, 2, . . . } with each row summing to s and each column summing to t. Equivalently, M(m, s;n, t) counts 2-way contingency tables of order m× n such that the row marginal sums are all s and the column marginal sums are all t. A third equivalent… (More)