{
  "id": "2208.10195",
  "version": "v1",
  "published": "2022-08-22T10:32:26.000Z",
  "updated": "2022-08-22T10:32:26.000Z",
  "title": "Maniplexes with automorphism group $\\textrm{PSL}_2(q)$",
  "authors": [
    "Dimitri Leemans",
    "Micael Toledo"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A maniplex of rank $n$ is a combinatorial object that generalises the notion of a rank $n$ abstract polytope. A maniplex with the highest possible degree of symmetry is called reflexible. In this paper we prove that there is a rank $4$ reflexible maniplex with automorphism group $\\textrm{PSL}_2(q)$ for infinitely many prime powers $q$, and that no reflexible maniplex of rank $n > 4$ exists that has $\\textrm{PSL}_2(q)$ as its full automorphism group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-22T10:32:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reflexible maniplex",
      "full automorphism group",
      "abstract polytope",
      "combinatorial object",
      "prime powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}