{
  "id": "1905.07535",
  "version": "v1",
  "published": "2019-05-18T04:40:48.000Z",
  "updated": "2019-05-18T04:40:48.000Z",
  "title": "Perfect 1-factorisations of $K_{16}$",
  "authors": [
    "Michael J. Gill",
    "Ian M. Wanless"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We report the results of a computer enumeration that found that there are 3155 perfect 1-factorisations (P1Fs) of the complete graph $K_{16}$. Of these, 89 have a non-trivial automorphism group (correcting an earlier claim of 88 by Meszka and Rosa). We also (i) describe a new invariant which distinguishes between the P1Fs of $K_{16}$, (ii) observe that the new P1Fs produce no atomic Latin squares of order 15 and (iii) record P1Fs for a number of large orders that exceed prime powers by one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-18T04:40:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-trivial automorphism group",
      "atomic latin squares",
      "earlier claim",
      "computer enumeration",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}