Higher Order Peak Algebras |
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Authors: | D Krob J -Y Thibon |
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Institution: | (1) Laboratoire d’Informatique, école Polytechnique, 91128 Palaiseau, France;(2) Institut Gaspard Monge, Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2, France |
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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.
Received November 19, 2004 |
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Keywords: | 05E05 16W30 |
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