Schubert polynomials and the Littlewood-Richardson rule

The decomposition of a product of two irreducible representations of a linear group Gl(N, ) is explicitly given by the Littlewood-Richardson rule, which amounts to finding how many Young tableaux satisfy certain conditions. We obtain more general multiplicities by generating vexillary permutations and by using partially symmetrical polynomials (Schubert polynomials).A la mémoire de S. Ulam, exemple et ami.