{
  "id": "2212.08452",
  "version": "v1",
  "published": "2022-12-16T12:54:22.000Z",
  "updated": "2022-12-16T12:54:22.000Z",
  "title": "The Birkhoff polytope of the groups $\\mathsf{F}_4$ and $\\mathsf{H}_4$",
  "authors": [
    "Mathieu Dutour Sikiric"
  ],
  "comment": "6 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We compute the set of facets of the polytope which is the convex hull of the Coxeter groups $\\mathsf{F}_4$ or $\\mathsf{H}_4$: For the group $\\mathsf{F}_4$ we found $2$ orbits of facets which contradicts previous results published in \\cite{birkhoff}. For the group $\\mathsf{H}_4$ we found $1063$ orbits of facets which provides a counterexample to the conjecture of \\cite{birkhoff}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-16T12:54:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff polytope",
      "convex hull",
      "coxeter groups",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}