{
  "abstract": "Discrete homotopy theory is a combinatorial homotopy theory defined for discrete objects. Barcelo--Severs--White conjectured that the homotopy groups of complements of $k$-parabolic subspace arrangements are isomorphic to the discrete homotopy groups of graphs associated with the Coxeter complexes. We show that this correspondence fails in general by giving a counterexample in degree two for the $4$-parabolic subspace arrangement of type $A_5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29690",
  "author_total": 1,
  "authors": [
    {
      "name": "So Yamagata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1hg8wfexwxqrv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29690",
  "fulltext_url": null,
  "id": "1hg8wfexwxqrv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29690",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223244100",
  "pdf_url": "https://arxiv.org/pdf/2610.29690",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1hg8wfexwxqrv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29690",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29690"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Discrete homotopy of graphs and $k$-parabolic subspace arrangements",
  "title_text": "Discrete homotopy of graphs and k-parabolic subspace arrangements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/1hg8wfexwxqrv",
  "venue": "arXiv",
  "versions": []
}