{
  "id": "0712.1755",
  "version": "v1",
  "published": "2007-12-11T16:20:07.000Z",
  "updated": "2007-12-11T16:20:07.000Z",
  "title": "Euler-Mahonian Statistics On Ordered Set Partitions (II)",
  "authors": [
    "Anisse Kasraoui",
    "Jiang Zeng"
  ],
  "comment": "27 pages,8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study statistics on ordered set partitions whose generating functions are related to $p,q$-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \\stein (Arxiv:math.CO/0605670). Our basic idea is to encode ordered partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. We also give a partition version of MacMahon's theorem on the equidistribution of the statistics inversion number and major index on words.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-11T16:20:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A30"
    ],
    "keywords": [
      "ordered set partitions",
      "euler-mahonian statistics",
      "statistics inversion number",
      "rich combinatorial properties",
      "encode ordered partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1755K"
    }
  }
}