{
  "id": "0808.3676",
  "version": "v3",
  "published": "2008-08-27T11:09:03.000Z",
  "updated": "2009-07-31T08:40:56.000Z",
  "title": "Pseudocyclic association schemes and strongly regular graphs",
  "authors": [
    "Akihiro Munemasa",
    "Takuya Ikuta"
  ],
  "comment": "corrected a typo",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated symmetric design is trivial. We present several non-amorphous examples, which are either cyclotomic association schemes, or their fusion schemes. Special properties of symmetric designs guarantee the existence of further fusions, and the two known non-amorphous association schemes of class 4 discovered by van Dam and by the authors, are recovered in this way. We also give another pseudocyclic non-amorphous association scheme of class 7 on GF(2^{21}), and a new pseudocyclic amorphous association scheme of class 5 on GF(2^{12}).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-31T08:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "11T22"
    ],
    "keywords": [
      "strongly regular graphs",
      "pseudocyclic non-amorphous association scheme",
      "symmetric designs guarantee",
      "cyclotomic association schemes",
      "amorphous pseudocyclic association schemes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3676M"
    }
  }
}