{
  "id": "1302.7313",
  "version": "v1",
  "published": "2013-02-28T20:50:16.000Z",
  "updated": "2013-02-28T20:50:16.000Z",
  "title": "A new proof for the Erdős-Ko-Rado Theorem for the alternating group",
  "authors": [
    "Bahman Ahmadi",
    "Karen Meagher"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A subset $S$ of the alternating group on $n$ points is {\\it intersecting} if for any pair of permutations $\\pi,\\sigma$ in $S$, there is an element $i\\in \\{1,\\dots,n\\}$ such that $\\pi(i)=\\sigma(i)$. We prove that if $S$ is intersecting, then $|S|\\leq \\frac{(n-1)!}{2}$. Also, we prove that if $n \\geq 5$, then the only sets $S$ that meet this bound are the cosets of the stabilizer of a point of $\\{1,\\dots,n\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-28T20:50:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C69"
    ],
    "keywords": [
      "alternating group",
      "erdős-ko-rado theorem",
      "permutations",
      "stabilizer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7313A"
    }
  }
}