{
  "abstract": "Fox $p$-colorings of knots and links admit a linear-algebraic description in terms of braid representations. For each braid $β\\in B_n$ we associate a representation $M : B_n \\to \\mathrm{GL}(n,\\mathbb{F}_p)$ such that Fox $p$-colorings of the closed braid $\\widehatβ$ correspond to fixed points of $M(β)$. As a consequence, $$ \\mathrm{Col}_p(\\widehatβ) = p^{\\dim \\ker(M(β)-I)}, $$ yielding an explicit formula for the number of Fox $p$-colorings of arbitrary knots and links. We apply the method to torus links and spiral links, obtaining explicit descriptions of their Fox 3-coloring spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29046",
  "author_total": 4,
  "authors": [
    {
      "name": "Neungjoo Goh"
    },
    {
      "name": "Suah Jeong"
    },
    {
      "name": "Seungbin Oh"
    },
    {
      "name": "Hyungkee Yoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ax9cpd19aaqz0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29046",
  "fulltext_url": null,
  "id": "ax9cpd19aaqz0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29046",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204955104",
  "pdf_url": "https://arxiv.org/pdf/2608.29046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ax9cpd19aaqz0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fox $p$-Colorings as Fixed Points of Braid Representations",
  "title_text": "Fox p-Colorings as Fixed Points of Braid Representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ax9cpd19aaqz0",
  "venue": "arXiv",
  "versions": []
}