{
  "id": "1808.01416",
  "version": "v1",
  "published": "2018-08-04T03:21:54.000Z",
  "updated": "2018-08-04T03:21:54.000Z",
  "title": "On a positivity conjecture in the character table of $S_n$",
  "authors": [
    "Sheila Sundaram"
  ],
  "comment": "37 pages, 6 tables",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "In previous work of this author it was conjectured that the sum of power sums $p_\\lambda,$ for partitions $\\lambda$ ranging over an interval $[(1^n), \\mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\\mu\\in [(n-4,1^4), (n)]$ or $\\mu\\in [(1^n), (3,1^{n-3})], $ or $\\mu=(3, 2^k, 1^r)$ when $k\\geq 1$ and $0\\leq r\\leq 2.$ Many new Schur positivity questions are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-04T03:21:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "20C05"
    ],
    "keywords": [
      "positivity conjecture",
      "character table",
      "schur positivity questions",
      "reverse lexicographic order",
      "power sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}