Duality between Quasi-Symmetrical Functions and the Solomon Descent Algebra Original Research Article

The ring QSym of quasi-symmetric functions is naturally the dual of the Solomon descent algebra. The product and the two coproducts of the first (extending those of the symmetric functions) correspond to a coproduct and two products of the second, which are defined by restriction from the symmetric group algebra. A consequence is that QSym is a free commutative algebra.