{
  "id": "math/0609704",
  "version": "v1",
  "published": "2006-09-25T17:02:56.000Z",
  "updated": "2006-09-25T17:02:56.000Z",
  "title": "Counting permutations by their runs up and down",
  "authors": [
    "E. Rodney Canfield",
    "Herbert S. Wilf"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We find a formula for the number of permutations of $[n]$ that have exactly $s$ runs up and down. The formula is at once terminating, asymptotic, and exact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-25T17:02:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16"
    ],
    "keywords": [
      "counting permutations",
      "asymptotic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9704C"
    }
  }
}