{
  "id": "2205.14078",
  "version": "v1",
  "published": "2022-05-27T16:21:31.000Z",
  "updated": "2022-05-27T16:21:31.000Z",
  "title": "q-Stirling numbers in type B",
  "authors": [
    "Bruce E. Sagan",
    "Joshua P. Swanson"
  ],
  "comment": "46 pages, 5 figures",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "Stirling numbers, which count partitions of a set and permutations in the symmetric group, have found extensive application in combinatorics, geometry, and algebra. We study analogues and q-analogues of these numbers corresponding to the Coxeter group of type B. In particular, we show how they are related to complete homogeneous and elementary symmetric polynomials; demonstrate how they q-count signed partitions and permutations; compute their ordinary, exponential, and q-exponential generating functions; and prove various identities about them. Ordered analogues of the q-Stirling numbers of the second kind have recently appeared in conjectures of Zabrocki and of Swanson--Wallach concerning the Hilbert series of certain super coinvariant algebras. We provide conjectural bases for these algebras and show that they have the correct Hilbert series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-27T16:21:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A18",
      "05A15",
      "05A30",
      "05E05",
      "05E16"
    ],
    "keywords": [
      "q-stirling numbers",
      "correct hilbert series",
      "super coinvariant algebras",
      "elementary symmetric polynomials",
      "q-count signed partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}