{
  "id": "0905.2899",
  "version": "v2",
  "published": "2009-05-18T14:43:53.000Z",
  "updated": "2009-05-20T17:27:57.000Z",
  "title": "Combinatorial interpretations of the Jacobi-Stirling numbers",
  "authors": [
    "Yoann Gelineau",
    "Jiang Zeng"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers. Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpretations for the Jacobi-Stirling numbers of both kinds, which provide a unified treatment of the combinatorial theories for the two previous sequences and also for the Stirling numbers of both kinds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-20T17:27:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "33C45",
      "05A10",
      "05A18",
      "34B24"
    ],
    "keywords": [
      "combinatorial interpretation",
      "jacobi-stirling numbers",
      "second kind",
      "classical central factorial numbers",
      "spectral theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2899G"
    }
  }
}