{
  "id": "2412.10214",
  "version": "v1",
  "published": "2024-12-13T15:38:02.000Z",
  "updated": "2024-12-13T15:38:02.000Z",
  "title": "Thron-type continued fractions (T-fractions) for some classes of increasing trees",
  "authors": [
    "Veronica Bitonti",
    "Bishal Deb",
    "Alan D. Sokal"
  ],
  "comment": "LaTeX2e, 62 pages including 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fractions with coefficients that are quasi-affine of period 2. Our proofs are based on bijections from trees to labeled Motzkin or Schr\\\"oder paths; these bijections extend the well-known bijection of Fran\\c{c}on--Viennot (1979) interpreted in terms of increasing binary trees. This work can also be viewed as a sequel to the recent work of Elvey Price and Sokal (2020), where they provide combinatorial interpretations for Thron-type continued fractions with coefficients that are affine. Towards the end of the paper, we conjecture an equidistribution of vincular patterns on permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-13T15:38:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A05",
      "05A15",
      "05A30",
      "05C05",
      "05C30",
      "30B70"
    ],
    "keywords": [
      "thron-type continued fractions",
      "increasing trees",
      "combinatorial interpretations",
      "t-fractions",
      "coefficients"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}