{
  "id": "1806.08323",
  "version": "v1",
  "published": "2018-06-21T17:07:51.000Z",
  "updated": "2018-06-21T17:07:51.000Z",
  "title": "On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix",
  "authors": [
    "Gary R. W. Greaves",
    "Pavlo Yatsyna"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For positive integers $e$, we find restrictions modulo $2^e$ on the coefficients of the characteristic polynomial $\\chi_S(x)$ of a Seidel matrix $S$. We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\\binom{e-2}{2}}$ (resp. $2^{\\binom{e-2}{2}+1}$) possibilities for the congruence class of $\\chi_S(x)$ modulo $2^e\\mathbb Z[x]$. As an application of these results we obtain an improvement to the upper bound for the number of equiangular lines in $\\mathbb R^{17}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-21T17:07:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "seidel matrix",
      "equiangular lines",
      "characteristic polynomial",
      "dimensions",
      "restrictions modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}