{
  "id": "math/0701096",
  "version": "v1",
  "published": "2007-01-03T15:21:09.000Z",
  "updated": "2007-01-03T15:21:09.000Z",
  "title": "A major index for matchings and set partitions",
  "authors": [
    "William Y. C Chen",
    "Ira M. Gessel",
    "Catherine H. Yan",
    "Arthur L. B. Yang"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a statistic $\\pmaj$ on partitions of $[n]=\\{1,2,..., n\\}$, and show that it is equidistributed with the number of 2-crossings over partitions of $[n]$ with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inversion number and major index.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-03T15:21:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18",
      "05A15"
    ],
    "keywords": [
      "major index",
      "set partitions",
      "permutation statistics inversion number",
      "minimal block elements",
      "maximal block elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1096C"
    }
  }
}