{
  "id": "1907.04416",
  "version": "v1",
  "published": "2019-07-09T21:09:52.000Z",
  "updated": "2019-07-09T21:09:52.000Z",
  "title": "Block-avoiding point sequencings of arbitrary length in Steiner triple systems",
  "authors": [
    "Douglas R. Stinson",
    "Shannon Veitch"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "An $\\ell$-good sequencing of an STS$(v)$ is a permutation of the points of the design such that no $\\ell$ consecutive points in this permutation contain a block of the design. We prove that, for every integer $\\ell \\geq 3$, there is an $\\ell$-good sequencing of any STS$(v)$ provided that $v$ is sufficiently large. We also prove some new nonexistence results for $\\ell$-good sequencings of STS$(v)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-09T21:09:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07"
    ],
    "keywords": [
      "steiner triple systems",
      "block-avoiding point sequencings",
      "arbitrary length",
      "nonexistence results",
      "permutation contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}