{
  "id": "1003.1688",
  "version": "v1",
  "published": "2010-03-08T18:00:16.000Z",
  "updated": "2010-03-08T18:00:16.000Z",
  "title": "Differences of Skew Schur Functions of Staircases with Transposed Foundations",
  "authors": [
    "Matthew Morin"
  ],
  "comment": "33 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the skew diagram $\\Delta_n$, which is the $180^\\circ$ rotation of the staircase diagram $\\delta_n = (n,n-1,n-2,...,2,1)$. We create a staircase with bad foundation by augmenting $\\Delta_n$ with another skew diagram, which we call the \\textit{foundation}. We consider pairs of staircases with bad foundation whose foundations are transposes of one another. Among these pairs, we show that the difference of the corresponding skew Schur functions is Schur-positive in the case when one of the foundations consists of either a one or two row diagram, or a hook diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-08T18:00:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "transposed foundations",
      "difference",
      "bad foundation",
      "skew diagram",
      "corresponding skew schur functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1688M"
    }
  }
}