{
  "id": "math/0312126",
  "version": "v1",
  "published": "2003-12-05T17:15:40.000Z",
  "updated": "2003-12-05T17:15:40.000Z",
  "title": "A Hopf algebra of parking functions",
  "authors": [
    "Jean-Christophe Novelli",
    "Jean-Yves Thibon"
  ],
  "comment": "AmsLatex, 14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-05T17:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hopf algebra",
      "complete homogeneous symmetric functions",
      "schur positive symmetric functions",
      "natural permutation representation",
      "specialization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12126N"
    }
  }
}