{
  "abstract": "The cubic pancake graphs are Cayley graphs over the symmetric group Sn generated by three prefix reversals. There is the folllowing open problem: characterize all the sets of three prefix reversals that generate Sn. Blanco and Golubyatnikov give a complete solution of the problem when any of the two smallest or the two largest lengths but n are included in a triple of prefix reversals. According to their conjectures, we give some conditions implying a triple of prefix reversals does not generate Sn. Moreover, Using the symmetric groups that can already be generated by three prefix reversals, we can derive some recurrence conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30892",
  "author_total": 4,
  "authors": [
    {
      "name": "Yexiao Lei"
    },
    {
      "name": "Jinxing Zhao"
    },
    {
      "name": "Ziyu Zhu"
    },
    {
      "name": "Yang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72xppp8j9faxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30892",
  "fulltext_url": null,
  "id": "72xppp8j9faxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30892",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223414684",
  "pdf_url": "https://arxiv.org/pdf/2610.30892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72xppp8j9faxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the generation of the symmetric group by index relations of three prefix reversals",
  "title_text": "On the generation of the symmetric group by index relations of three prefix reversals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/72xppp8j9faxq",
  "venue": "arXiv",
  "versions": []
}