Algorithms for constructing [formula omitted]-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 ≼ λ ≼ R * . In this bijection, the tableau of shape λ , the insertion tableau, has content S and the tableau of shape λ * , 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 R * , respectively.