A Hopf algebra of parking functions

Details A Hopf algebra of parking functions A Hopf algebra of parking functions

2003-12-05

arxiv.org/abs/math/0312126v1

Mathematics

Combinatorics

AmsLatex, 14 pages

Scientific paper

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 $(f_n)$. We prove that $(f_n)$ 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.

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