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Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
G´erard H.E. Duchamp1, Florent Hivert2, Jean-Christophe Novelli3, and Jean-Yves Thibon3
1Institut Galilée, LIPN, UMR CNRS 7030, F-93430 Villetaneuse, France
ghed@lipn.univ-paris13.fr
2LITIS, Université de Rouen; 76801 Saint ´Etienne du Rouvray, France
hivert@univ-rouen.fr
3Institut Gaspard-Monge, Université Paris-Est, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
{novelli, jyt}@univ-mlv.fr
Annals of Combinatorics 15 (4) pp.655-673 December, 2011
AMS Subject Classification: 05E05, 16T30
Abstract:
We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.
Keywords: noncommutative symmetric functions, quasi-symmetric functions, combinatorial Hopf algebras

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