If the moments of a probability measure on R 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 (fn). We prove that (fn) 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.Comment: AmsLatex, 14 page
