On (0, 1)-matrices with prescribed row and column sum vectors

Given partitions R and S with the same weight, the Robinson-Schensted-Knuth correspondence establishes a bijection between the class A ( R , S ) of (0, 1)-matrices with row sum R and column sum S and pairs of Young tableaux of conjugate shapes λ and λ ∗ , with S ≼ λ ≼ R ∗ . An algorithm for constructing a matrix in A ( R , S ) whose insertion tableau has a prescribed shape λ , with S ≼ λ ≼ R ∗ , is provided. We generalize some recent constructions due to R. Brualdi for the extremal cases λ = S and λ = R ∗ .