{
  "id": "2406.09666",
  "version": "v1",
  "published": "2024-06-14T02:30:43.000Z",
  "updated": "2024-06-14T02:30:43.000Z",
  "title": "Graphs of Reduced Words and Some Connections",
  "authors": [
    "Praise Adeyemo"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The family of graphs of reduced words of a certain subcollection of permutations in the union $\\cup_{n\\geq 4}\\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with consecutive fixed points. A closed formula for counting the vertices of each member of the family is given and the vertex-degree polynomials for the graphs with their generating series is realised. Lastly, some isomorphisms of these graphs with various combinatorial objects are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-14T02:30:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reduced words",
      "connections",
      "hook cycle type",
      "combinatorial objects",
      "subcollection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}