{
  "id": "math/0603520",
  "version": "v3",
  "published": "2006-03-21T19:07:08.000Z",
  "updated": "2006-07-05T20:32:17.000Z",
  "title": "Alternating permutations and symmetric functions",
  "authors": [
    "Richard P. Stanley"
  ],
  "comment": "37 pages, one figure. Correction of gap in the proof of Corollary 6.4, and some further minor corrections",
  "categories": [
    "math.CO"
  ],
  "abstract": "We use the theory of symmetric functions to enumerate various classes of alternating permutations w of {1,2,...,n}. These classes include the following: (1) both w and w^{-1} are alternating, (2) w has certain special shapes, such as (m-1,m-2,...,1), under the RSK algorithm, (3) w has a specified cycle type, and (4) w has a specified number of fixed points. We also enumerate alternating permutations of a multiset. Most of our formulas are umbral expressions where after expanding the expression in powers of a variable E, E^k is interpreted as the Euler number E_k. As a small corollary, we obtain a combinatorial interpretation of the coefficients of an asymptotic expansion appearing in Ramanujan's Lost Notebook.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-07-05T20:32:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A40",
      "05E05"
    ],
    "keywords": [
      "symmetric functions",
      "ramanujans lost notebook",
      "special shapes",
      "rsk algorithm",
      "specified cycle type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3520S"
    }
  }
}