{
  "id": "math/9806057",
  "version": "v1",
  "published": "1998-06-10T19:13:51.000Z",
  "updated": "1998-06-10T19:13:51.000Z",
  "title": "Flag-symmetry of the poset of shuffles and a local action of the symmetric group",
  "authors": [
    "Rodica Simion",
    "Richard P. Stanley"
  ],
  "comment": "34 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the poset of shuffles introduced by Greene in 1988 is flag-symmetric, and we describe a \"local\" permutation action of the symmetric group on the maximal chains which is closely related to the flag symmetric function of the poset. A key tool is provided by a new labeling of the maximal chains of a poset of shuffles, which is also used to give bijective proofs of enumerative properties originally obtained by Greene. In addition we define a monoid of multiplicative functions on all posets of shuffles and describe this monoid in terms of a new operation on power series in two variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-06-10T19:13:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05E05",
      "05E25"
    ],
    "keywords": [
      "symmetric group",
      "local action",
      "flag-symmetry",
      "maximal chains",
      "flag symmetric function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......6057S"
    }
  }
}