{
  "id": "2305.09457",
  "version": "v1",
  "published": "2023-05-16T14:18:43.000Z",
  "updated": "2023-05-16T14:18:43.000Z",
  "title": "Permutations with few inversions",
  "authors": [
    "Anders Claesson",
    "Atli Fannar Franklín",
    "Einar Steingrímsson"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C(x)$ is the generating function for the Catalan numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-16T14:18:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutations",
      "inversions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}