The concatenation product of permutations enjoys many nice properties with respect to Schubert calculus; that is, from a combinatorial point of view, with respect to the Lascoux-Schützenberger calculus of Schubert polynomials. We give explicit formulas for the product of the Schubert cycles (resp. polynomials) which are associated to the corresponding permutations with general Schubert cycles (resp. polynomials). Those formulas complete the partial known results about the combinatorics of intersections products on flag manifolds (Monk's formula, generalized Pieri formula of Lascoux and Schützenberger, some properties of vexillary permutations).
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