{
  "id": "1405.6462",
  "version": "v1",
  "published": "2014-05-26T05:16:25.000Z",
  "updated": "2014-05-26T05:16:25.000Z",
  "title": "Cayley Graph on Symmetric Group Generated by Elements Fixing $k$ Points",
  "authors": [
    "Kok Bin Wong",
    "Terry Lau",
    "Cheng Yeaw Ku"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{S}_{n}$ be the symmetric group on $[n]=\\{1, \\ldots, n\\}$. The $k$-point fixing graph $\\mathcal{F}(n,k)$ is defined to be the graph with vertex set $\\mathcal{S}_{n}$ and two vertices $g$, $h$ of $\\mathcal{F}(n,k)$ are joined if and only if $gh^{-1}$ fixes exactly $k$ points. In this paper, we derive a recurrence formula for the eigenvalues of $\\mathcal{F}(n,k)$. Then we apply our result to determine the sign of the eigenvalues of $\\mathcal{F}(n,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-26T05:16:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "cayley graph",
      "elements fixing",
      "point fixing graph",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6462W"
    }
  }
}