Algorithms for constructing (0,1)-matrices with prescribed row and column sum vectors

There is a bijection between the class A(R, S) of (0, 1)-matrices with row sum vector R and column sum vector S and pairs of Young tableaux of conjugate shapes lambda and lambda* with S <=lambda <= R*. In this bijection, the tableau of shape lambda, the insertion tableau, has content S and the tableau of shape lambda*, the recording tableau, has content R. Using a Ryser-like algorithm, we give canonical constructions for matrices in A(R, S) whose insertion tableaux have shape lambda = S and R*, respectively. (c) 2006 Elsevier B.V. All rights reserved.