{
  "id": "2009.05785",
  "version": "v1",
  "published": "2020-09-12T13:15:33.000Z",
  "updated": "2020-09-12T13:15:33.000Z",
  "title": "Number of Triangulations of a Möbius Strip",
  "authors": [
    "Bazier-Matte Véronique",
    "Huang Ruiyan",
    "Luo Hanyi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Consider a M\\\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a M\\\"obius strip with $n$ chosen points on its edge is given by $4^{n-1}+\\binom{2n-2}{n-1}$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the M\\\"obius strip.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-12T13:15:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60"
    ],
    "keywords": [
      "möbius strip",
      "triangulation",
      "chosen points",
      "maximal collection",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}