A Hopf algebra of parking functions
arXiv:math/0312126
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 $\SG_n$ 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.
AmsLatex, 14 pages