{
  "id": "1805.10998",
  "version": "v1",
  "published": "2018-05-28T16:01:16.000Z",
  "updated": "2018-05-28T16:01:16.000Z",
  "title": "On certain combinatorial expansions of the Legendre-Stirling numbers",
  "authors": [
    "Shi-Mei Ma",
    "Jun Ma",
    "Yeong-Nan Yeh"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. In this paper, we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain combinatorial expansions of the Legendre-Stirling numbers of both kinds. Moreover, we present grammatical descriptions of the Jacobi-Stirling numbers of both kinds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-28T16:01:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "legendre-stirling numbers",
      "combinatorial expansions",
      "legendre differential expressions",
      "second kind",
      "spectral theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}