A Hopf algebra of parking functions

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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.
AmsLatex, 14 pages

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/69485

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312126
 http://arxiv.org/abs/math/0312126

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arXiv