{
  "id": "1407.5766",
  "version": "v3",
  "published": "2014-07-22T07:28:26.000Z",
  "updated": "2020-07-27T10:16:52.000Z",
  "title": "Steiner triple systems without parallel classes",
  "authors": [
    "Darryn Bryant",
    "Daniel Horsley"
  ],
  "comment": "5 pages, 0 figures. This version fixes a minor error in the journal version of the paper where we had neglected to say that two sum-zero triples must be removed before the additional triples in $\\mathcal{B}^\\infty \\cup \\mathcal{B}^*$ are added to create the Steiner triple system",
  "categories": [
    "math.CO"
  ],
  "abstract": "We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to $3 \\pmod{6}$. The only previously known examples have order $15$ or $21$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-06T07:08:50.000Z",
      "comment": "5 pages, 0 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2020-07-27T10:16:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07"
    ],
    "keywords": [
      "parallel classes",
      "construct steiner triple systems",
      "orders congruent",
      "infinite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5766B"
    }
  }
}