{
  "abstract": "A fusion ring is said to be vanishing if one of its multiplication matrices has determinant zero. We classify all vanishing fusion rings of rank four. We then provide a more explicit classification in the integral case, which leads to new consequences: there are infinitely many nonisomorphic simple integral vanishing fusion rings of rank four and no simple integral fusion ring of rank four is 1-Frobenius. We also classify all Burnside fusion rings of rank four.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22000",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingcheng Dong"
    },
    {
      "name": "Sebastien Palcoux"
    },
    {
      "name": "Arnaud Plessis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28ktr9trv5mnb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22000",
  "fulltext_url": null,
  "id": "28ktr9trv5mnb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22000",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.NT"
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      "arxiv",
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    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7222621717",
  "pdf_url": "https://arxiv.org/pdf/2610.22000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28ktr9trv5mnb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.22000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Classification of vanishing fusion rings of rank four",
  "title_text": "Classification of vanishing fusion rings of rank four",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/28ktr9trv5mnb",
  "venue": "arXiv",
  "versions": []
}