{
  "id": "1204.2589",
  "version": "v2",
  "published": "2012-04-11T23:13:11.000Z",
  "updated": "2013-01-24T13:15:08.000Z",
  "title": "1-Overlap Cycles for Steiner Triple Systems",
  "authors": [
    "Victoria Horan",
    "Glenn Hurlbert"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing elements of a combinatorial family in a specific manner, and Godbole invented the following generalization of these in 2010. 1-overlap cycles require a set of strings to be ordered so that the last letter of one string is the first letter of the next. In this paper, we prove the existence of 1-overlap cycles for automorphism free Steiner triple systems of each possible order. Since Steiner triple systems have the property that each block can be represented uniquely by a pair of points, these 1-overlap cycles can be compressed by omitting non-overlap points to produce rank two universal cycles on such designs, expanding on the results of Dewar.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-24T13:15:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68R15",
      "05B05"
    ],
    "keywords": [
      "automorphism free steiner triple systems",
      "universal cycles",
      "disk erasure codes",
      "first letter",
      "gray codes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2589H"
    }
  }
}