{
  "id": "2405.12672",
  "version": "v1",
  "published": "2024-05-21T10:50:51.000Z",
  "updated": "2024-05-21T10:50:51.000Z",
  "title": "Small examples of mosaics of combinatorial designs",
  "authors": [
    "Vedran Krčadinac"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give the first example of a mosaic of three combinatorial designs with distinct parameters $2$-$(13,3,1)$, $2$-$(13,4,2)$, and $2$-$(13,6,5)$. Furthermore, we give examples of mosaics of $2$-$(9,3,2)$ designs that are not resolvable, thereby answering a question posed by M. Wiese and H. Boche. Finally, we give an example of a mosaic of projective planes of order $3$ that cannot be obtained by tiling groups with difference sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-21T10:50:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B20",
      "05B05"
    ],
    "keywords": [
      "combinatorial designs",
      "small examples",
      "first example",
      "distinct parameters",
      "difference sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}