The admissible interval for the invariant factors of a product of matrices

It is well known that Littlewood-Richardson sequences give a combinatorial characterization for the factors of a product of two matrices over a principal ideal domain. Given partitions a and c, let LR (a,c) be the set of part ions b for which at least one Littlewood-Richardson sequence of type (a,b,c) exists. I. Zaballa has shown in [20] that LR(a,c) has a minimal element w and a maximal element n, with respect to the order of majorization, depending on a and c. In general, LR(a,c) is not the whole [w,n]. Here a combinatorial algorithm is provided for constructing all the elements of LR(a,c). This algorithm consists in starting with the minimal Littlewood-Richardson sequence of shape c/a and successively modifying it until the maximal Littlewood-Richardson sequence of shape c/a is achieved. Also explicit bijections between Littlewood-Richardson sequences of conjugate shape and weight and between Littlewood-Richardson sequences of dual shape and equal weight are shape and weight and between Littlewood-Richardson sequences of dual shape and equal weight are presented. The bijections are defined by means of permutations of Littlewood-Richardson sequencesAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga