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

There is a bijection between the class A(R,S)A(R,S) of (0,1)(0,1)-matrices with row sum vector R and column sum vector S   and pairs of Young tableaux of conjugate shapes λλ and λ*λ* with S≼λ≼R*S≼λ≼R*. In this bijection, the tableau of shape λλ, the insertion tableau, has content S   and the tableau of shape λ*λ*, the recording tableau, has content R  . Using a Ryser-like algorithm, we give canonical constructions for matrices in A(R,S)A(R,S) whose insertion tableaux have shape λ=Sλ=S and R*R*, respectively.