Generalized descent patterns in permutations and associated Hopf algebras

Authors:
Jean-Christophe Novelli;Christophe Reutenauer;Jean-Yves Thibon
Affiliations:
Institut Gaspard Monge, Université Paris-Est Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France;LaCIM, Université du Québec í Montréal, CP 8888, Succ. Centre-ville, Montréal (Québec) H3C 3P8, Canada;Institut Gaspard Monge, Université Paris-Est Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
Venue:
European Journal of Combinatorics
Year:
2011

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Abstract

Descents in permutations or words are defined from the relative position of two consecutive letters. We investigate a statistic involving patterns of k consecutive letters, and show that it leads to Hopf algebras generalizing noncommutative symmetric functions and quasi-symmetric functions.