An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums

Abstract

We count mxn non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n grow.

57 pages, results strengthened, proofs simplified somewhat