{
  "id": "1305.2438",
  "version": "v1",
  "published": "2013-05-10T20:49:51.000Z",
  "updated": "2013-05-10T20:49:51.000Z",
  "title": "Charge on tableaux and the poset of k-shapes",
  "authors": [
    "Luc Lapointe",
    "Maria Elena Pinto"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A poset on a certain class of partitions known as k-shapes was recently introduced to provide a combinatorial rule for the expansion of a (k-1)-Schur functions into k-Schur functions at t=1. The main ingredient in this construction was a bijection, which we call the weak bijection, that associates to a k-tableau a pair made out of a (k-1)-tableau and a path in the poset of k-shapes. We define here a concept of charge on k-tableaux (which conjecturally gives a combinatorial interpretation for the expansion coefficients of Hall-Littlewood polynomials into k-Schur functions), and show that it is compatible in the standard case with the weak bijection. In particular, we obtain that the usual charge of a standard tableau of size n is equal to the sum of the charges of its corresponding paths in the poset of k-shapes, for k=2,3...n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-10T20:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "k-schur functions",
      "weak bijection",
      "main ingredient",
      "combinatorial rule",
      "standard tableau"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2438L"
    }
  }
}