Carlos Fonseca; Ricardo Mamede;
On (0,1)-matrices with prescribed row and column sum vectors
Given partitions R and S with the same weight, 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 (P,Q) of Young tableaux of conjugate shapes l and l*, with S<l< R*. An algorithm for constructing a matrix in A(R,S) whose insertion tableaux has a prescribed shape l, with S<l< R*, is provided. We generalize some recent constructions due to R. Brualdi for the extremal cases l=S and l=R*.
Pré-publicações do Departamento de Matemática da Universidade de Coimbra