{
  "id": "2406.12796",
  "version": "v1",
  "published": "2024-06-18T17:02:47.000Z",
  "updated": "2024-06-18T17:02:47.000Z",
  "title": "Extensions of Steiner triple systems",
  "authors": [
    "Giovanni Falcone",
    "Agota Figula",
    "Mario Galici"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a powerful method for constructing Steiner triple systems containing Veblen points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T17:02:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07",
      "20N05",
      "51E10"
    ],
    "keywords": [
      "extensions",
      "steiner loop",
      "triple systems containing veblen points",
      "steiner triple system corresponds",
      "steiner triple systems containing veblen"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}