{
  "id": "1610.02077",
  "version": "v1",
  "published": "2016-10-06T21:38:32.000Z",
  "updated": "2016-10-06T21:38:32.000Z",
  "title": "A property of the Birkhoff polytope",
  "authors": [
    "Barbara Baumeister",
    "Frieder Ladisch"
  ],
  "comment": "10 pages, pdflatex (with biblatex)",
  "categories": [
    "math.CO",
    "math.GR",
    "math.RT"
  ],
  "abstract": "The Birkhoff polytope $B_n$ is the convex hull of all $n\\times n$ permutation matrices in $\\mathbb{R}^{n\\times n}$. We compute the combinatorial symmetry group of the Birkhoff polytope. A representation polytope is the convex hull of some finite matrix group $G\\leq \\operatorname{GL}(d,\\mathbb{R})$. We show that the group of permutation matrices is essentially the only finite matrix group which yields a representation polytope with the same face lattice as the Birkhoff polytope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-06T21:38:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B15",
      "52B05",
      "52B12",
      "20B25",
      "20C15",
      "05E18"
    ],
    "keywords": [
      "birkhoff polytope",
      "finite matrix group",
      "convex hull",
      "permutation matrices",
      "representation polytope"
    ],
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}