An extension of Brualdi’s algorithm for the construction of -matrices with prescribed row and column sum vectors

Given partitions R and S with the same weight and S ⪯ R ∗ , 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 with conjugate shape λ and λ ∗ , with S ⪯ λ ⪯ R ∗ . We give a canonical construction for matrices in A ( R , S ) whose insertion tableau has a prescribed shape λ , with S ⪯ λ ⪯ R ∗ . This algorithm generalizes some recent constructions due to R. Brualdi for the extremal cases λ = S and λ = R ∗ (using a Ryser-like algorithm), and due to C.M. da Fonseca and R. Mamede for particular cases of λ .