{
  "id": "2207.05210",
  "version": "v1",
  "published": "2022-07-11T22:06:57.000Z",
  "updated": "2022-07-11T22:06:57.000Z",
  "title": "A Simple Proof that Major Index and Inversions are Equidistributed",
  "authors": [
    "Michael J. Collins"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a short proof of MacMahon's classic result that the number of permutations with $k$ inversions equals the number whose major index (sum of positions at which descents occur) is $k$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-11T22:06:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05"
    ],
    "keywords": [
      "major index",
      "simple proof",
      "macmahons classic result",
      "short proof",
      "descents occur"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}