{
  "id": "1708.04974",
  "version": "v1",
  "published": "2017-08-14T20:22:58.000Z",
  "updated": "2017-08-14T20:22:58.000Z",
  "title": "A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over $\\mathbb{Z}/p\\mathbb{Z}$",
  "authors": [
    "Jeremy F. Alm",
    "Andrew Ylvisaker"
  ],
  "categories": [
    "math.CO",
    "cs.DS"
  ],
  "abstract": "Proper relation algebras can be constructed using $\\mathbb{Z}/p\\mathbb{Z}$ as a base set using a method due to Comer. The cycle structure of such an algebra must, in general, be determined \\emph{a posteriori}, normally with the aid of a computer. In this paper, we give an improved algorithm for checking the cycle structure that reduces the time complexity from $\\mathcal{O}(p^2)$ to $\\mathcal{O}(p)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-14T20:22:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G15",
      "11Y16"
    ],
    "keywords": [
      "cycle structure",
      "fast coset-translation algorithm",
      "comer relation algebras",
      "proper relation algebras",
      "time complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}