{
  "id": "1410.7087",
  "version": "v1",
  "published": "2014-10-26T21:29:12.000Z",
  "updated": "2014-10-26T21:29:12.000Z",
  "title": "Bounds on Kronecker and $q$-binomial coefficients",
  "authors": [
    "Igor Pak",
    "Greta Panova"
  ],
  "comment": "12 pages. This paper is an extension of parts of the earlier paper \"Bounds on the Kronecker coefficients\" arXiv:1406.2988, which also contains stability results",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We present a lower bound on the Kronecker coefficients of the symmetric group via the characters of $S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial coefficients $\\binom{n}{k}_q$ as polynomials in $q$ to derive sharp bounds on the differences of their consecutive coefficients",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-26T21:29:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial coefficients",
      "extend sylvesters unimodality",
      "symmetric group",
      "lower bound",
      "kronecker coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7087P"
    }
  }
}