{
  "annotation_id": "d630b7ba-e843-49aa-8f25-1a908744de63",
  "date_created": "2026-03-02T18:02:16.980000Z",
  "date_modified": "2026-03-02T18:02:16.980000Z",
  "file_hash": "97aab4384be4a70c42abc8c7e982b5d5c81ba65b9a577d3e73a6f297ebdc93b7",
  "private": false,
  "record": {
    "abstract": "We consider the numbers arising in the problem of normal ordering of\nexpressions in canonical boson creation and annihilation operators. We treat a\ngeneral form of a boson string which is shown to be associated with\ngeneralizations of Stirling and Bell numbers. The recurrence relations and\nclosed-form expressions (Dobiski-type formulas) are obtained for these\nquantities by both algebraic and combinatorial methods. By extensive use of\nmethods of combinatorial analysis we prove the equivalence of the\naforementioned problem to the enumeration of special families of graphs. This\nlink provides a combinatorial interpretation of the numbers arising in this\nnormal ordering problem.",
    "arxiv_id": "quant-ph/0505180",
    "authors": [
      "M A Mendez",
      "P Blasiak",
      "K A Penson"
    ],
    "categories": [
      "quant-ph",
      "math.CO"
    ],
    "doi": "10.1063/1.1990120",
    "journal_ref": "J. Math. Phys. 46, 083511 (2005)",
    "title": "Combinatorial approach to generalized Bell and Stirling numbers and   boson normal ordering problem",
    "url": "https://arxiv.org/abs/quant-ph/0505180"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d365d4df-4ddb-403a-ac9e-43eee9e51727",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}