{
  "id": "2210.08629",
  "version": "v1",
  "published": "2022-10-16T20:16:23.000Z",
  "updated": "2022-10-16T20:16:23.000Z",
  "title": "A Note On $\\ell$-Rauzy Graphs for the Infinite Fibonacci Word",
  "authors": [
    "Rajavel Praveen M",
    "Rama R"
  ],
  "comment": "10 pages, 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The $\\ell$-Rauzy graph of order $k$ for any infinite word is a directed graph in which an arc $(v_1,v_2)$ is formed if the concatenation of the word $v_1$ and the suffix of $v_2$ of length $k-\\ell$ is a subword of the infinite word. In this paper, we consider one of the important aperiodic recurrent words, the infinite Fibonacci word for discussion. We prove a few basic properties of the $\\ell$-Rauzy graph of the infinite Fibonacci word. We also prove that the $\\ell$-Rauzy graphs for the infinite Fibonacci word are strongly connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-16T20:16:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite fibonacci word",
      "rauzy graph",
      "infinite word",
      "important aperiodic recurrent words",
      "basic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}