{
  "abstract": "Let $(W,S)$ be a Coxeter system of finite rank, let $T$ be its set of reflections and let $c \\in W$ be a Coxeter element. For $x$ in the interval $[1,c]_T$ of the absolute order, let $P(x)$ be the subgroup generated by the reflections $t\\le_T x$. We prove that $x$ is a Coxeter element of $P(x)$ with respect to the canonical Coxeter generators of $P(x)$, that $P(x)$ is generated by the factors of any reduced reflection factorization of $x$, and that the Hurwitz action on the reduced reflection factorizations of $x$ is transitive. The proof reduces the general case to the case of a Coxeter system whose Coxeter matrix has entries in $\\{1,2,3,\\infty\\}$, which was treated by Hubery and Krause.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19755",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrick Wegener"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/371tpspcngsbh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19755",
  "fulltext_url": null,
  "id": "371tpspcngsbh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19755",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7222237531",
  "pdf_url": "https://arxiv.org/pdf/2610.19755",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/371tpspcngsbh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19755",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19755"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Prefixes of Coxeter elements are Coxeter elements of the reflection subgroups they generate",
  "title_text": "Prefixes of Coxeter elements are Coxeter elements of the reflection subgroups they generate",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/371tpspcngsbh",
  "venue": "arXiv",
  "versions": []
}