{
  "id": "1807.08384",
  "version": "v1",
  "published": "2018-07-22T23:34:58.000Z",
  "updated": "2018-07-22T23:34:58.000Z",
  "title": "Lattices with many congruences are planar",
  "authors": [
    "Gábor Czédli"
  ],
  "comment": "10 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $L$ be an $n$-element finite lattice. We prove that if $L$ has strictly more than $2^{n-5}$ congruences, then $L$ is planar. This result is sharp, since for each natural number $n\\geq 8$, there exists a non-planar lattice with exactly $2^{n-5}$ congruences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-22T23:34:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06B10"
    ],
    "keywords": [
      "congruences",
      "element finite lattice",
      "non-planar lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}