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

Abstract

There is a bijection between the class A (R, S) of (0, 1)-matrices with row sum vector R and column sum vector S and pairs of Young tableaux of conjugate shapes λ and λ* with S {precedes or equal to} λ {precedes or equal to} Rz.ast;. In this bijection, the tableau of shape λ, the insertion tableau, has content S and the tableau of shape λz.ast;, the recording tableau, has content R. Using a Ryser-like algorithm, we give canonical constructions for matrices in A (R, S) whose insertion tableaux have shape λ = S and Rz.ast;, respectively. © 2006 Elsevier B.V. All rights reserved.