{
  "id": "2411.16307",
  "version": "v2",
  "published": "2024-11-25T11:52:39.000Z",
  "updated": "2025-01-08T12:05:01.000Z",
  "title": "On the number of small Steiner triple systems with Veblen points",
  "authors": [
    "Mario Galici",
    "Giuseppe Filippone"
  ],
  "journal": "Discrete Math. 348, No. 1, Article ID 114294, 13 p. (2025)",
  "doi": "10.1016/j.disc.2024.114294",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The concept of Schreier extensions of loops was introduced in the general case in [11] and, more recently, it has been explored in the context of Steiner loops in [6]. In the latter case, it gives a powerful method for constructing Steiner triple systems containing Veblen points. Counting all Steiner triple systems of order v is an open problem for v>21. In this paper, we investigate the number of Steiner triple systems of order 19, 27 and 31 containing Veblen points and we present some examples.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-08T12:05:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07",
      "20N05",
      "51E10"
    ],
    "keywords": [
      "small steiner triple systems",
      "triple systems containing veblen points",
      "steiner triple systems containing veblen",
      "constructing steiner triple systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}