{
  "id": "math/0511501",
  "version": "v1",
  "published": "2005-11-20T21:56:16.000Z",
  "updated": "2005-11-20T21:56:16.000Z",
  "title": "The distance of a permutation from a subgroup of S_n",
  "authors": [
    "Richard G. E. Pinch"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the problem of computing the distance of a given permutation from a subgroup $H$ of $S_n$ is in general NP-complete, even under the restriction that $H$ is elementary Abelian of exponent 2. The problem is shown to be polynomial-time equivalent to a problem related to finding a maximal partition of the edges of an Eulerian directed graph into cycles and this problem is in turn equivalent to the standard NP-complete problem of Boolean satisfiability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-20T21:56:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B40",
      "05C38",
      "20B35",
      "68Q25"
    ],
    "keywords": [
      "permutation",
      "standard np-complete problem",
      "general np-complete",
      "maximal partition",
      "elementary abelian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11501P"
    }
  }
}