Abstract
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.
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