{
  "id": "1710.03896",
  "version": "v1",
  "published": "2017-10-11T04:01:46.000Z",
  "updated": "2017-10-11T04:01:46.000Z",
  "title": "Distribution of descents in matchings",
  "authors": [
    "Gene B. Kim"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "The distribution of descents in a fixed conjugacy class of $S_n$ is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed point free involutions). This paper provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-11T04:01:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "60F05",
      "60C05",
      "62E20"
    ],
    "keywords": [
      "distribution",
      "fixed point free involutions",
      "asymptotic normality theorem",
      "fixed conjugacy class",
      "major indices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}