Higher order peak algebras
Combinatorics
2013-02-12 v1
Abstract
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.
Cite
@article{arxiv.math/0411407,
title = {Higher order peak algebras},
author = {Daniel Krob and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:math/0411407},
year = {2013}
}
Comments
20 pages, AMS LaTex