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Duality between quasi-symmetric functions and the Solomon descent algebra. (English) Zbl 0838.05100
Summary: 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.

MSC:
05E05 Symmetric functions and generalizations
20C30 Representations of finite symmetric groups
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