{
  "id": "2408.14139",
  "version": "v1",
  "published": "2024-08-26T09:36:46.000Z",
  "updated": "2024-08-26T09:36:46.000Z",
  "title": "Greedy base sizes for sporadic simple groups",
  "authors": [
    "Coen del Valle"
  ],
  "comment": "9 pages, 3 tables",
  "categories": [
    "math.GR"
  ],
  "abstract": "A base for a permutation group $G$ acting on a set $\\Omega$ is a sequence $\\mathcal{B}$ of points of $\\Omega$ such that the pointwise stabiliser $G_{\\mathcal{B}}$ is trivial. Denote the minimum size of a base for $G$ by $b(G)$. There is a natural greedy algorithm for constructing a base of relatively small size; denote by $\\mathcal{G}(G)$ the maximum size of a base it produces. Motivated by a long-standing conjecture of Cameron, we determine $\\mathcal{G}(G)$ for every almost simple primitive group $G$ with socle a sporadic simple group, showing that $\\mathcal{G}(G)=b(G)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-26T09:36:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sporadic simple group",
      "greedy base sizes",
      "natural greedy algorithm",
      "permutation group",
      "simple primitive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}