{
  "id": "math/0507544",
  "version": "v2",
  "published": "2005-07-26T17:16:56.000Z",
  "updated": "2013-01-22T20:01:11.000Z",
  "title": "A Combinatorial Interpretation for the coefficients in the Kronecker Product $s_{(n-p,p)}\\ast s_λ$ (Multiplicities in the Kronecker Product $s_{(n-p,p)}\\ast s_λ$)",
  "authors": [
    "Cristina M. Ballantine",
    "Rosa C. Orellana"
  ],
  "comment": "29 pages, A typo in Corollary 4.13 was corrected (this was Corollary 4.16 in the previous version). The title has been changed",
  "journal": "S\\'em. Lothar. Combin. 54A (2005/07), Art. B54Af",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we give a combinatorial interpretation for the coefficient of $s_{\\nu}$ in the Kronecker product $s_{(n-p,p)}\\ast s_{\\lambda}$, where $\\lambda=(\\lambda_1, ..., \\lambda_{\\ell(\\lambda)})\\vdash n$, if $\\ell(\\lambda)\\geq 2p-1$ or $\\lambda_1\\geq 2p-1$; that is, if $\\lambda$ is not a partition inside the $2(p-1)\\times 2(p-1)$ square. For $\\lambda$ inside the square our combinatorial interpretation provides an upper bound for the coefficients. In general, we are able to combinatorially compute these coefficients for all $\\lambda$ when $n>(2p-2)^2$. We use this combinatorial interpretation to give characterizations for multiplicity free Kronecker products. We have also obtained some formulas for special cases.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-22T20:01:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C30"
    ],
    "keywords": [
      "combinatorial interpretation",
      "coefficient",
      "multiplicity free kronecker products",
      "special cases",
      "partition inside"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}