{
  "id": "1803.02377",
  "version": "v1",
  "published": "2018-03-06T19:01:04.000Z",
  "updated": "2018-03-06T19:01:04.000Z",
  "title": "The equivariant volumes of the permutahedron",
  "authors": [
    "Federico Ardila",
    "Anna Schindler",
    "Andrés R. Vindas-Meléndez"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the action of the symmetric group $S_n$ on the permutahedron $\\Pi_n$. We prove that if $\\sigma$ is a permutation of $S_n$ which has $m$ cycles of lengths $l_1, \\ldots, l_m$, then the subpolytope of $\\Pi_n$ fixed by $\\sigma$ has normalized volume $n^{m-2} \\gcd(l_1, \\ldots, l_m)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-06T19:01:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "52A38",
      "52B15"
    ],
    "keywords": [
      "equivariant volumes",
      "permutahedron",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}