{
  "abstract": "We study systems of moves and states in the sense of [JNW21] on certain bipartite graphs, and the associated homomorphisms from the commutator subgroups of right-angled Coxeter groups to $\\mathbb Z$. We give examples of right-angled Coxeter groups whose graphs do not satisfy the legal system criterion, but contain finite index right-angled Coxeter subgroups whose graphs admit legal systems. We also provide a family of examples of graphs without legal systems, where no sequence of the considered graph operations yields a graph with a legal system. Moreover, we show that for a bipartite graph and an orbit of non-empty states under the bipartite system of moves, the associated homomorphism from the commutator subgroup of the right-angled Coxeter group to $\\mathbb Z$ has finitely generated kernel if and only if the system is legal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37641",
  "author_total": 2,
  "authors": [
    {
      "name": "Kasia Jankiewicz"
    },
    {
      "name": "Shayan Miri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0var4hkg17a52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37641",
  "fulltext_url": null,
  "id": "0var4hkg17a52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37641",
  "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"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7224084942",
  "pdf_url": "https://arxiv.org/pdf/2610.37641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0var4hkg17a52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Algebraic fiberings of right-angled Coxeter groups on bipartite cone graphs",
  "title_text": "Algebraic fiberings of right-angled Coxeter groups on bipartite cone graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/0var4hkg17a52",
  "venue": "arXiv",
  "versions": []
}