{
  "id": "1905.12364",
  "version": "v1",
  "published": "2019-05-29T12:10:49.000Z",
  "updated": "2019-05-29T12:10:49.000Z",
  "title": "Separators - a new statistic for permutations",
  "authors": [
    "Eli Bagno",
    "Estrella Eisenberg",
    "Shulamit Reches",
    "Moriah Sigron"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A digit $\\pi_j$ in a permutation $\\pi=[\\pi_1,\\ldots,\\pi_n]\\in S_n$ is defined to be a separator of $\\pi$ if by omitting it from $\\pi$ we get a new $2-$block. In this work we introduce a new statistic, the number of separators, on the symmetric group $S_n$ and calculate its distribution over $S_n$. We also provide some enumerative and asymptotic results regarding this statistic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-29T12:10:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation",
      "symmetric group",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}