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Higher Order Peak Algebras
D. Krob1 and J.-Y. Thibon2
1Laboratoire d'Informatique, École Polytechnique, 91128 Palaiseau, France
dk@lix.polytechnique.fr
2Institut Gaspard Monge, Université Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur- Marne, 77454 Marne-la-Vallée cedex 2, France
jyt@univ-mlv.fr
Annals of Combinatorics 9 (4) p.411-430 December, 2005
AMS Subject Classification: 05E05, 16W30
Abstract:
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients.

Keywords: Noncommutative symmetric functions, descent algebras, peak algebras

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