{
  "id": "math/0203101",
  "version": "v2",
  "published": "2002-03-11T18:25:32.000Z",
  "updated": "2002-03-27T19:22:54.000Z",
  "title": "Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)",
  "authors": [
    "Marcelo Aguiar",
    "Frank Sottile"
  ],
  "comment": "12 pages, 2 .eps figures. (minor revisions) Extended abstract for Formal Power Series and Algebraic Combinatorics, Melbourne, July 2002",
  "categories": [
    "math.CO",
    "math.QA",
    "math.RA"
  ],
  "abstract": "We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-03-27T19:22:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "06A11",
      "16W30"
    ],
    "keywords": [
      "malvenuto-reutenauer hopf algebra",
      "extended abstract",
      "permutations",
      "explicit formulas",
      "cofree coalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3101A"
    }
  }
}