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 @l and @l^* with [email protected][email protected]@?R^*. In this bijection, the tableau of shape @l, the insertion tableau, has content S and the tableau of shape @l^*, 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 @l=S and R^*, respectively.