{
  "id": "1007.1207",
  "version": "v2",
  "published": "2010-07-07T17:57:55.000Z",
  "updated": "2010-10-22T19:50:02.000Z",
  "title": "The sorting index",
  "authors": [
    "T. Kyle Petersen"
  ],
  "comment": "14 pages, minor changes, new references added",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-22T19:50:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "sorting index",
      "natural combinatorial descriptions",
      "reflection length generating functions",
      "finite coxeter group",
      "bivariate polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.1207P"
    }
  }
}