{
  "id": "2501.03003",
  "version": "v1",
  "published": "2025-01-06T13:26:37.000Z",
  "updated": "2025-01-06T13:26:37.000Z",
  "title": "Irredundant bases for soluble groups",
  "authors": [
    "Sofia Brenner",
    "Coen del Valle",
    "Colva M. Roney-Dougal"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $\\Delta$ be a finite set and $G$ be a subgroup of $\\operatorname{Sym}(\\Delta)$. An irredundant base for $G$ is a sequence of points of $\\Delta$ yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that $G$ is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for $G$. Moreover, we disprove a conjecture of Seress on the maximum length of an irredundant base constructed by the natural greedy algorithm, and prove Cameron's Greedy Conjecture for $|G|$ odd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-06T13:26:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B15",
      "20D10",
      "20E15"
    ],
    "keywords": [
      "irredundant base",
      "soluble groups",
      "maximum length",
      "camerons greedy conjecture",
      "natural greedy algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}