{
  "id": "math/0502456",
  "version": "v1",
  "published": "2005-02-22T15:09:58.000Z",
  "updated": "2005-02-22T15:09:58.000Z",
  "title": "Commutative Hopf algebras of permutations and trees",
  "authors": [
    "F. Hivert",
    "J. -C. Novelli",
    "J. -Y. Thibon"
  ],
  "comment": "18 pages, LaTEX",
  "categories": [
    "math.CO"
  ],
  "abstract": "We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its non-commutative dual is realized in three different ways, in particular as the Grossman-Larson algebra of heap ordered trees. Extensions to endofunctions, parking functions, set partitions, planar binary trees and rooted forests are discussed. Finally, we introduce one-parameter families interpolating between different structures constructed on the same combinatorial objects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-22T15:09:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutations",
      "planar binary trees",
      "cocommutative hopf algebras",
      "combinatorial structures",
      "grossman-larson algebra"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2456H"
    }
  }
}