{
  "id": "2401.13356",
  "version": "v1",
  "published": "2024-01-24T10:34:03.000Z",
  "updated": "2024-01-24T10:34:03.000Z",
  "title": "Properties of Steiner triple systems of order 21",
  "authors": [
    "Grahame Erskine",
    "Terry S. Griggs"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Properties of the 62,336,617 Steiner triple systems of order 21 with a non-trivial automorphism group are examined. In particular, there are 28 which have no parallel class, six that are 4-chromatic, five that are 3-balanced, 20 that avoid the mitre, 21 that avoid the crown, one that avoids the hexagon and two that avoid the prism. All systems contain the grid. None have a block intersection graph that is 3-existentially closed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T10:34:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07"
    ],
    "keywords": [
      "steiner triple systems",
      "properties",
      "block intersection graph",
      "non-trivial automorphism group",
      "systems contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}