{
  "id": "2309.00092",
  "version": "v1",
  "published": "2023-08-31T19:20:40.000Z",
  "updated": "2023-08-31T19:20:40.000Z",
  "title": "Irredundant bases for the symmetric group",
  "authors": [
    "Colva M. Roney-Dougal",
    "Peiran Wu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "An irredundant base of a group $G$ acting faithfully on a finite set $\\Gamma$ is a sequence of points in $\\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in $G$, terminating at the trivial subgroup. Suppose that $G$ is $\\operatorname{S}_n$ or $\\operatorname{A}_n$ acting primitively on $\\Gamma$, and that the point stabiliser is primitive in its natural action on $n$ points. We prove that the maximum size of an irredundant base of $G$ is $O\\left(\\sqrt{n}\\right)$, and in most cases $O\\left((\\log n)^2\\right)$. We also show that these bounds are best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-31T19:20:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B15",
      "20D06",
      "20E15"
    ],
    "keywords": [
      "irredundant base",
      "symmetric group",
      "finite set",
      "point stabiliser",
      "pointwise stabiliser subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}