{
  "id": "1603.09645",
  "version": "v1",
  "published": "2016-03-31T15:39:35.000Z",
  "updated": "2016-03-31T15:39:35.000Z",
  "title": "$3$-pyramidal Steiner Triple Systems",
  "authors": [
    "Marco Buratti",
    "Gloria Rinaldi",
    "Tommaso Traetta"
  ],
  "comment": "14 pages, 0 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A design is said to be $f$-pyramidal when it has an automorphism group which fixes $f$ points and acts sharply transitively on all the others. The problem of establishing the set of values of $v$ for which there exists an $f$-pyramidal Steiner triple system of order $v$ has been deeply investigated in the case $f=1$ but it remains open for a special class of values of $v$. The same problem for the next possible $f$, which is $f=3$, is here completely solved: there exists a $3$-pyramidal Steiner triple system of order $v$ if and only if $v\\equiv7,9,15$ (mod $24$) or $v\\equiv 3, 19$ (mod 48).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T15:39:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07",
      "G.2.0"
    ],
    "keywords": [
      "pyramidal steiner triple system",
      "special class",
      "remains open",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}