{
  "abstract": "We show that for $n \\geq 6$ each element of the commutator subgroup in the symmetric group $\\mathfrak{S}_n$ resp. in the signed symmetric group $(\\mathbb{Z}/2\\mathbb{Z})^n\\rtimes\\mathfrak{S}_n$ is the commutator of two $n$-cycles resp. the commutator of two $n$-cycles with a negative sign product; with one exception. If $n \\equiv 2$ $\\mathrm{mod}~4$, the element $-\\mathrm{id}$ of $(\\mathbb{Z}/2\\mathbb{Z})^n\\rtimes\\mathfrak{S}_n$ is not such a commutator. In the language of Coxeter groups, this yields a description of commutators of Coxeter elements in types $A$ and $B$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24518",
  "author_total": 3,
  "authors": [
    {
      "name": "Philipp Bader"
    },
    {
      "name": "Bernhard Böhmler"
    },
    {
      "name": "Patrick Wegener"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rxqtz158eavh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24518",
  "fulltext_url": null,
  "id": "0rxqtz158eavh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24518",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214043970",
  "pdf_url": "https://arxiv.org/pdf/2609.24518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rxqtz158eavh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Commutators of signed $n$-cycles",
  "title_text": "Commutators of signed n-cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/0rxqtz158eavh",
  "venue": "arXiv",
  "versions": []
}