A Hopf algebra of parking functions
Combinatorics
2007-05-23 v1
Abstract
If the moments of a probability measure on are interpreted as a specialization of complete homogeneous symmetric functions, its free cumulants are, up to sign, the corresponding specializations of a sequence of Schur positive symmetric functions . We prove that is the Frobenius characteristic of the natural permutation representation of on the set of prime parking functions. This observation leads us to the construction of a Hopf algebra of parking functions, which we study in some detail.
Keywords
Cite
@article{arxiv.math/0312126,
title = {A Hopf algebra of parking functions},
author = {Jean-Christophe Novelli and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:math/0312126},
year = {2007}
}
Comments
AmsLatex, 14 pages