{
  "id": "2308.08254",
  "version": "v1",
  "published": "2023-08-16T09:47:04.000Z",
  "updated": "2023-08-16T09:47:04.000Z",
  "title": "Cameron-Liebler sets in permutation groups",
  "authors": [
    "Jozefien D'haeseleer",
    "Karen Meagher",
    "Venkata Raghu Tej Pantangi"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Consider a group $G$ acting on a set $\\Omega$, the vector $v_{a,b}$ is a vector with the entries indexed by the elements of $G$, and the $g$-entry is 1 if $g$ maps $a$ to $b$, and zero otherwise. A $(G,\\Omega)$-Cameron-Liebler set is a subset of $G$, whose indicator function is a linear combination of elements in $\\{v_{a, b}\\ :\\ a, b \\in \\Omega\\}$. We investigate Cameron-Liebler sets in permutation groups, with a focus on constructions of Cameron-Liebler sets for 2-transitive groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-16T09:47:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05E15"
    ],
    "keywords": [
      "cameron-liebler set",
      "permutation groups",
      "indicator function",
      "linear combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}