{
  "id": "2307.00570",
  "version": "v1",
  "published": "2023-07-02T13:37:31.000Z",
  "updated": "2023-07-02T13:37:31.000Z",
  "title": "Some identities involving $q$-Stirling numbers of the second kind in type B",
  "authors": [
    "Ming-Jian Ding",
    "Jiang Zeng"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The recent interest in $q$-Stirling numbers of the second kind in type B prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which turns out to be a $q$-analogue of an identity due to Bagno, Biagioli and Garber. We provide a combinatorial proof of this identity and an analytical proof of a more general identity for colored permutations. In addition, we prove some $q$-identities about the $q$-Stirling numbers of the second kind in types A, B and D.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-02T13:37:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A18",
      "05A19"
    ],
    "keywords": [
      "second kind",
      "stirling numbers",
      "carlitzs major",
      "eulerian numbers",
      "combinatorial proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}