{
  "abstract": "For a Coxeter system $(W,S)$ of finite rank and an involutive automorphism $\\ast:W\\to W$ which preserves $S$, we prove that the length-generating function $\\sum_{z\\in\\mathbf{I}_{W,\\ast}}q^{\\ell(z)}$ of the set of $\\ast$-twisted involutions is rational. We derive recurrence relations analogous to the well-known recurrence relations expressing the growth series $W(q):=\\sum_{w\\in W}q^{\\ell(w)}$ in terms of the growth series $W_I(q)$ of the parabolic subgroups of $W$. Our result extends to any subset $\\mathcal{C}$ of $\\ast$-twisted involutions that is closed under $\\ast$-twisted conjugation. We use these recurrence relations to give an alternative proof of a power-series identity for twisted involutions due to Lusztig.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08000",
  "author_total": 1,
  "authors": [
    {
      "name": "Ronald de Man"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0cyfm424svkdt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08000",
  "fulltext_url": null,
  "id": "0cyfm424svkdt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08000",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7211997986",
  "pdf_url": "https://arxiv.org/pdf/2609.08000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0cyfm424svkdt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Length-generating functions for twisted involutions of Coxeter groups",
  "title_text": "Length-generating functions for twisted involutions of Coxeter groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0cyfm424svkdt",
  "venue": "arXiv",
  "versions": []
}