{
  "id": "2412.17065",
  "version": "v1",
  "published": "2024-12-22T15:32:33.000Z",
  "updated": "2024-12-22T15:32:33.000Z",
  "title": "Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5",
  "authors": [
    "Stepan Orevkov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $f(m,n)$ be the number of primitive lattice triangulations of an $m \\times n$ rectangle. We express the limits $\\lim_n f(m,n)^{1/n}$ for $m = 4$ and $m=5$ in terms of certain systems of Fredholm integral equations on generating functions (the case $m\\le3$ was treated in a previous paper). Solving these equations numerically, we compute approximate values of these limits with a rather high precision.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-22T15:32:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotics",
      "fredholm integral equations",
      "approximate values",
      "high precision",
      "primitive lattice triangulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}