{
  "id": "1204.3215",
  "version": "v1",
  "published": "2012-04-14T20:42:45.000Z",
  "updated": "2012-04-14T20:42:45.000Z",
  "title": "Overlap Cycles for Steiner Quadruple Systems",
  "authors": [
    "Victoria Horan",
    "Glenn Hurlbert"
  ],
  "comment": "24 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is will known that Steiner quadruple systems of order v, or SQS(v), exist if and only if v = 2, 4 mod 6. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole. Using Hanani's SQS constructions, we show that for every v = 2, 4 mod 6 with v > 4 there exists an SQS(v) that admits a 1-overlap cycle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-14T20:42:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "05B05"
    ],
    "keywords": [
      "steiner quadruple systems",
      "overlap cycles",
      "universal cycles",
      "hananis sqs constructions",
      "cyclic gray code"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.3215H"
    }
  }
}