{
  "id": "2211.05475",
  "version": "v1",
  "published": "2022-11-10T10:41:38.000Z",
  "updated": "2022-11-10T10:41:38.000Z",
  "title": "Signed Graphs and Signed Cycles of Hyperoctahedral Groups",
  "authors": [
    "Ryo Uchiumi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "J. D\\'enes gave a bijection between the set of edge-labeled trees on $\\{1,\\ldots,n\\}$ and the set of sequences consisting of $n-1$ transpositions such that the product is an $n$-cycle. As a corollary, D\\'enes proved that the number of trees on $\\{1,\\ldots,n\\}$ is equal to the number of representations of an $n$-cycle by means of product of $n-1$ transpositions. In this article, we consider an analogy of D\\'enes' results for signed trees and hyperoctahedral groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T10:41:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05C22",
      "05C05"
    ],
    "keywords": [
      "hyperoctahedral groups",
      "signed graphs",
      "signed cycles",
      "transpositions",
      "denes gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}