{
  "id": "1909.09101",
  "version": "v1",
  "published": "2019-09-19T17:18:03.000Z",
  "updated": "2019-09-19T17:18:03.000Z",
  "title": "Block-avoiding point sequencings of Mendelsohn triple systems",
  "authors": [
    "Donald L. Kreher",
    "Douglas R. Stinson",
    "Shannon Veitch"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A cyclic ordering of the points in a Mendelsohn triple system of order $v$ (or MTS$(v)$) is called a sequencing. A sequencing $D$ is $\\ell$-good if there does not exist a triple $(x,y,z)$ in the MTS$(v)$ such that (1) the three points $x,y,$ and $z$ occur (cyclically) in that order in $D$; and (2) $\\{x,y,z\\}$ is a subset of $\\ell$ cyclically consecutive points of $D$. In this paper, we prove some upper bounds on $\\ell$ for MTS$(v)$ having $\\ell$-good sequencings and we prove that any MTS$(v)$ with $v \\geq 7$ has a $3$-good sequencing. We also determine the optimal sequencings of every MTS$(v)$ with $v \\leq 10$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-19T17:18:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B07"
    ],
    "keywords": [
      "mendelsohn triple system",
      "block-avoiding point sequencings",
      "upper bounds",
      "optimal sequencings",
      "cyclically consecutive points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}