{
  "abstract": "(This is a reprint of the thesis published in the Transactions of the Conference Devoted to the 90th Anniversary Of Alexei A. Lyapunov, Novosibirsk, October 8-12, 2001, pages 323-327). The number of ways for partial $n$-quasigroups of order $4$ to be extended to $n$-quasigroups is investigated. Upper bounds on the number of $n$-quasigroups of order $4$ are obtained. The asymptotic $3^{n+1}2^{2^n+1}$ of that number is established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03116",
  "author_total": 2,
  "authors": [
    {
      "name": "Denis S. Krotov"
    },
    {
      "name": "Vladimir N. Potapov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a0209x05vmtz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03116",
  "fulltext_url": null,
  "id": "4a0209x05vmtz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03116",
  "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|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7208777759",
  "pdf_url": "https://arxiv.org/pdf/2609.03116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a0209x05vmtz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the reconstruction of $n$-quasigroups of order $4$ and upper bounds on their number",
  "title_text": "On the reconstruction of n-quasigroups of order $4$ and upper bounds on their number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/4a0209x05vmtz",
  "venue": "arXiv",
  "versions": []
}