{
  "id": "1704.00851",
  "version": "v1",
  "published": "2017-04-04T01:55:59.000Z",
  "updated": "2017-04-04T01:55:59.000Z",
  "title": "Some Schubert shenanigans",
  "authors": [
    "Richard P. Stanley"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a conjectured evaluation of the determinant of a certain matrix $\\tilde{D}(n,k)$. The entries of $\\tilde{D}(n,k)$ are either 0 or specializations $\\mathfrak{S}_w(1,\\dots,1)$ of Schubert polynomials. The conjecture implies that the weak order of the symmetric group $S_n$ has the strong Sperner property. A number of peripheral results and problems are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-04T01:55:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E99",
      "05D05"
    ],
    "keywords": [
      "schubert shenanigans",
      "strong sperner property",
      "weak order",
      "symmetric group",
      "peripheral results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}