{
  "id": "1412.0444",
  "version": "v1",
  "published": "2014-12-01T12:05:48.000Z",
  "updated": "2014-12-01T12:05:48.000Z",
  "title": "Hall-Littlewood symmetric functions via Yamanouchi toppling game",
  "authors": [
    "Robert Cori",
    "Pasquale Petrullo",
    "Domenico Senato"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We define a solitary game, the Yamanouchi toppling game, on any connected graph of n vertices. The game arises from the well-known chip-firing game when the usual relation of equivalence defined on the set of all configurations is replaced by a suitable partial order. The set all firing sequences of length m that the player is allowed to perform in the Yamanouchi toppling game is shown to be in bijection with all standard Young tableaux whose shape is a partition of the integer m with at most n-1 parts. The set of all configurations that a player can obtain from a starting configuration is encoded in a suitable formal power series. When the graph is the simple path and each monomial of the series is replaced by a suitable Schur polynomial, we prove that such a series reduces to Hall-Littlewod symmetric polynomials. The same series provides a combinatorial description of orthogonal polynomials when the monomials are replaced by products of moments suitably modified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-01T12:05:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "91A46",
      "05E18",
      "33C45"
    ],
    "keywords": [
      "yamanouchi toppling game",
      "hall-littlewood symmetric functions",
      "hall-littlewod symmetric polynomials",
      "suitable formal power series",
      "configuration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0444C"
    }
  }
}