Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

Gerard H. E. Duchamp (1) , Florent Hivert (2) , Jean-Christophe Novelli (3) , Jean-Yves Thibon (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Combinatoire [math.CO]

Gerard H. E. Duchamp, Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited. Annals of Combinatorics, 2011, 15 (4), pp.655-673. ⟨10.1007/s00026-011-0115-4⟩. ⟨hal-00826640⟩