{
  "id": "1011.2737",
  "version": "v3",
  "published": "2010-11-11T18:58:38.000Z",
  "updated": "2011-02-08T08:34:09.000Z",
  "title": "Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields",
  "authors": [
    "Graeme Taylor"
  ],
  "doi": "10.1016/j.jalgebra.2011.02.009",
  "categories": [
    "math.NT"
  ],
  "abstract": "We determine all Hermitian $\\mathcal{O}_{\\Q(\\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15\\}. To do so, we generalise charged signed graphs to $\\mathcal{L}$-graphs for appropriate finite sets $\\mathcal{L}$, and classify all $\\mathcal{L}$-graphs satisfying the same eigenvalue constraints. We find that, as in the integer case, any such matrix / graph is contained in a maximal example with all eigenvalues $\\pm2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-08T08:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C22",
      "11C20"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "cyclotomic matrices",
      "appropriate finite sets",
      "eigenvalue constraints",
      "maximal example"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2737T"
    }
  }
}