{
  "id": "1808.02581",
  "version": "v1",
  "published": "2018-08-07T23:19:10.000Z",
  "updated": "2018-08-07T23:19:10.000Z",
  "title": "The commuting complex of the symmetric group with bounded number of $p$-cycles",
  "authors": [
    "Cihan Bahran"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GR",
    "math.CO",
    "math.RT"
  ],
  "abstract": "For a fixed prime $p$, we consider a filtration of the commuting complex of elements of order $p$ in the symmetric group $\\mathfrak{S}_n$. The filtration is obtained by imposing successively relaxed bounds on the number of disjoint $p$-cycles in the cycle decomposition of the elements. We show that each term in the filtration becomes highly acyclic as $n$ increases. We use $\\mathbf{FI}$-modules in the proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-07T23:19:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "commuting complex",
      "bounded number",
      "filtration",
      "cycle decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}