{
  "id": "2404.01465",
  "version": "v1",
  "published": "2024-04-01T20:25:10.000Z",
  "updated": "2024-04-01T20:25:10.000Z",
  "title": "Mahonian-Stirling statistics for partial permutations",
  "authors": [
    "Ming-Jian Ding",
    "Jiang Zeng"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a suitable analogue of MacMahon's major index. We provide such a major index, namely, the corresponding maj and inv statistics are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs generalizing Deb and Sokal's alternating Laguerre digraph interpretation of some special Jacobi-Rogers polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-01T20:25:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial permutations",
      "mahonian-stirling statistics",
      "sokals alternating laguerre digraph interpretation",
      "haglund-remmel-wilson type identity",
      "macmahons major index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}