{
  "id": "2009.01410",
  "version": "v1",
  "published": "2020-09-03T01:54:23.000Z",
  "updated": "2020-09-03T01:54:23.000Z",
  "title": "Encoding labelled $p$-Riordan graphs by words and pattern-avoiding permutations",
  "authors": [
    "Kittitat Iamthong",
    "Ji-Hwan Jung",
    "Sergey Kitaev"
  ],
  "comment": "To appear in Graphs and Combinatorics, 14 pages, 1 fiugure",
  "categories": [
    "math.CO"
  ],
  "abstract": "The notion of a $p$-Riordan graph generalizes that of a Riordan graph, which, in turn, generalizes the notions of a Pascal graph and a Toeplitz graph. In this paper we introduce the notion of a $p$-Riordan word, and show how to encode $p$-Riordan graphs by $p$-Riordan words. For special important cases of Riordan graphs (the case $p=2$) and oriented Riordan graphs (the case $p=3$) we provide alternative encodings in terms of pattern-avoiding permutations and certain balanced words, respectively. As a bi-product of our studies, we provide an alternative proof of a known enumerative result on closed walks in the cube.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-03T01:54:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "pattern-avoiding permutations",
      "riordan word",
      "riordan graph generalizes",
      "special important cases",
      "oriented riordan graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}