{
  "id": "2002.08535",
  "version": "v1",
  "published": "2020-02-20T02:29:19.000Z",
  "updated": "2020-02-20T02:29:19.000Z",
  "title": "The fraction of an $S_n$-orbit on a hyperplane",
  "authors": [
    "Brendan Pawlowski"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Huang, McKinnon, and Satriano conjectured that if $v \\in \\mathbb{R}^n$ has distinct coordinates and $n \\geq 3$, then a hyperplane through the origin other than $\\sum_i x_i = 0$ contains at most $2\\lfloor n/2 \\rfloor (n-2)!$ of the vectors obtained by permuting the coordinates of $v$. We prove this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-20T02:29:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperplane",
      "distinct coordinates",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}