Higher order peak algebras

Details Higher order peak algebras Higher order peak algebras

2004-11-18

arxiv.org/abs/math/0411407v1

Mathematics

Combinatorics

20 pages, AMS LaTex

Scientific paper

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, 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.

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