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Parking Functions and Descent Algebras
Jean-Christophe Novelli, Jean-Yves Thibon
Institut Gaspard Monge, Université de Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur- Marne, 77454 Marne-la-Vallée cedex 2, France
{novelli, jyt}@univ-mlv.fr
Annals of Combinatorics 11 (1) p.59-68 March, 2007
AMS Subject Classification: 05E05, 16W30
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.
Keywords: parking functions, descent algebras, quasi-symmetric functions


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