{
  "id": "1703.06314",
  "version": "v1",
  "published": "2017-03-18T16:08:18.000Z",
  "updated": "2017-03-18T16:08:18.000Z",
  "title": "Representability of Lyndon-Maddux relation algebras",
  "authors": [
    "Jeremy F. Alm"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "In Alm-Hirsch-Maddux (2016), relation algebras $\\mathfrak{L}(q,n)$ were defined that generalize Roger Lyndon's relation algebras from projective lines, so that $\\mathfrak{L}(q,0)$ is a Lyndon algebra. In that paper, it was shown that if $q>2304n^2+1$, $\\mathfrak{L}(q,n)$ is representable, and if $q<2n$, $\\mathfrak{L}(q,n)$ is not representable. In the present paper, we reduced this gap by proving that if $q\\geq n(\\log n)^{1+\\varepsilon}$, $\\mathfrak{L}(q,n)$ is representable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-18T16:08:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03G15",
      "05D40"
    ],
    "keywords": [
      "lyndon-maddux relation algebras",
      "representability",
      "generalize roger lyndons relation algebras",
      "lyndon algebra",
      "projective lines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}