{
  "abstract": "A Gray code for $S_n$ is \\emph{genlex} when words sharing a suffix are consecutive. We determine the genlex Gray codes for $S_n$ that use the fewest possible operations: Zaks' recursion generalises to a superfactorial family of such codes, and no code outside this family attains the minimum. Every code in the family closes into a cycle, and the cycle is invariant under a group of left translations, cyclic of order $n$ or dihedral of order $2n$ according to an explicit criterion on the operations. In the pancake graph the family reduces to a single member, the classical Zaks order; with respect to the standard parabolic chain of $W(A_{n-1})$, that order attains one extreme of total Coxeter length.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13214",
  "author_total": 1,
  "authors": [
    {
      "name": "Yehonathan Sharvit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aazqwbkv256q7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13214",
  "fulltext_url": null,
  "id": "aazqwbkv256q7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13214",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213305765",
  "pdf_url": "https://arxiv.org/pdf/2609.13214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aazqwbkv256q7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Genlex Gray codes for $S_n$ with the fewest operations: classification and symmetry",
  "title_text": "Genlex Gray codes for S_n with the fewest operations: classification and symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/aazqwbkv256q7",
  "venue": "arXiv",
  "versions": []
}