{
  "abstract": "Let \\(\\mathbb{F}_q\\) be a finite field with \\(q>7\\). Zhi-Wei Sun conjectured that for every \\(a_0\\in\\mathbb{F}_q\\), there is a circular permutation \\((a_1,\\dots,a_{q-1})\\) of non-zero elements of \\(\\mathbb{F}_q\\) such that \\(a_0+a_i a_{i+1}\\) is primitive for \\(1\\le i\\le q-1\\), where \\(a_q=a_1\\). In this paper, we confirm this conjecture for \\(q>18\\,888\\,871\\). For \\(a_0=0\\), the conclusion holds for all \\(q>4\\). For \\(a_0\\ne0\\), we apply the Chvátal--Erdős theorem to obtain a Hamilton cycle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06289",
  "author_total": 2,
  "authors": [
    {
      "name": "Xin-Qi Luo"
    },
    {
      "name": "Yue-Feng She"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22sf70etjfqx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06289",
  "fulltext_url": null,
  "id": "22sf70etjfqx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06289",
  "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|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7220661809",
  "pdf_url": "https://arxiv.org/pdf/2610.06289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22sf70etjfqx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Conjecture on Circular Permutations over Finite Fields",
  "title_text": "A Conjecture on Circular Permutations over Finite Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/22sf70etjfqx8",
  "venue": "arXiv",
  "versions": []
}