{
  "id": "2305.07728",
  "version": "v1",
  "published": "2023-05-12T18:48:04.000Z",
  "updated": "2023-05-12T18:48:04.000Z",
  "title": "Incidences and tilings",
  "authors": [
    "Sergey Fomin",
    "Pavlo Pylyavskyy"
  ],
  "comment": "70 pages, 79 figures",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\\\"obius, and so on, can be interpreted as special cases of a single \"master theorem\" that involves an arbitrary tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing the known ones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-12T18:48:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E14",
      "14N20",
      "51M15",
      "51A20"
    ],
    "keywords": [
      "real/complex linear incidence geometry",
      "special cases",
      "master theorem",
      "incidence theorems",
      "quadrilateral tiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 70,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}