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

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