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Parking functions and descent algebras. (English) Zbl 1115.05095
Summary: We show that the notion of parkization of a word, a variant of the classical standardization, allows us to introduce an internal product on the Hopf algebra of parking functions. Its Catalan subalgebra is stable under this operation and contains the descent algebra as a left ideal.

MSC:
05E05 Symmetric functions and generalizations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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