{
  "id": "2307.05198",
  "version": "v1",
  "published": "2023-07-11T12:08:47.000Z",
  "updated": "2023-07-11T12:08:47.000Z",
  "title": "An Inversion Statistic on the Hyperoctahedral Group",
  "authors": [
    "Hasan Arslan",
    "Alnour Altoum",
    "Hilal Karakus Arslan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we introduce an inversion statistic on the hyperoctahedral group $B_n$ by using an decomposition of a positive root system of this reflection group. Then we prove some combinatorial properties for the inversion statistic. We establish an enumeration system on the group $B_n$ and give an efficient method to uniquely derive any group element known its enumeration order with the help of the inversion table. In addition, we prove that the \\textit{flag-major index} is equi-distributed with this inversion statistic on $B_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-11T12:08:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A19",
      "20F55"
    ],
    "keywords": [
      "inversion statistic",
      "hyperoctahedral group",
      "enumeration order",
      "positive root system",
      "combinatorial properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}