{
  "id": "1811.00857",
  "version": "v1",
  "published": "2018-11-02T13:46:54.000Z",
  "updated": "2018-11-02T13:46:54.000Z",
  "title": "Normally ordered forms of powers of differential operators and their combinatorics",
  "authors": [
    "Emmanuel Briand",
    "Samuel A. Lopes",
    "Mercedes Rosas"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We investigate the combinatorics of the general formulas for the powers of the operator $h \\partial^k$, where $h$ is a central element of a ring and $\\partial$ is a differential operator. This generalizes previous work on the powers of operators $h \\partial$. New formulas for the generalized Stirling numbers are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T13:46:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normally ordered forms",
      "differential operator",
      "combinatorics",
      "central element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}