{
  "id": "2004.14007",
  "version": "v1",
  "published": "2020-04-29T08:08:03.000Z",
  "updated": "2020-04-29T08:08:03.000Z",
  "title": "Quelques Éléments de Combinatoire des Matrices de $SL_2(\\mathbb{Z})$",
  "authors": [
    "Flavien Mabilat"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A Theorem of V.Ovsienko characterizes sequences of positive integers $(a_{1},a_{2},\\ldots,a_{n})$ such that the $(2\\times2)$-matrix $\\begin{pmatrix} a_{n} & -1 \\\\ 1 & 0 \\end{pmatrix}\\cdots \\begin{pmatrix} a_{1} & -1 \\\\ 1 & 0 \\end{pmatrix}$ is equal to $\\pm Id$. In this paper, we study matrices $M$ such that some properties verified by the previous equation are still true when we replace $\\pm Id$ by $\\pm M$. We also give a combinatorial description of the solutions of this equation when $M=\\begin{pmatrix} 0 & -1 \\\\ 1 & 0 \\end{pmatrix}$ in terms of dissections of convex polygons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-29T08:08:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatoire",
      "ovsienko characterizes sequences",
      "study matrices",
      "combinatorial description",
      "convex polygons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}