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Parking Functions and Descent Algebras

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Abstract.

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.

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Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée cedex 2, France

    Jean-Christophe Novelli & Jean-Yves Thibon

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  1. Jean-Christophe Novelli
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  2. Jean-Yves Thibon
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Correspondence to Jean-Christophe Novelli.

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Received March 1, 2005

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Novelli, JC., Thibon, JY. Parking Functions and Descent Algebras. Ann. Comb. 11, 59–68 (2007). https://doi.org/10.1007/s00026-007-0305-2

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  • DOI: https://doi.org/10.1007/s00026-007-0305-2

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