{
  "abstract": "It is shown that, as $n\\to\\infty$, the logarithm of the number of decompositions into cycles of the $n$-dimensional Boolean cube $E^n$ is \\[ 2^n(\\ln n-1+o(1)), \\] and the logarithm of the number of Hamiltonian cycles in $E^n$ is at least \\[ 2^{n-1}(\\ln n-1+o(1)). \\] It is proved that, in $E^n$, every perfect matching whose edges belong to at most $k$ directions can be extended to a Hamiltonian cycle for every $n\\geq n_0(k)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Diskretn. Anal. Issled. Oper., Ser. 1, 8:2 (2001), 52-62",
  "arxiv": "2610.11941",
  "author_total": 2,
  "authors": [
    {
      "name": "A. L. Perezhogin"
    },
    {
      "name": "V. N. Potapov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dr4n3kgjb99fm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11941",
  "fulltext_url": null,
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  "landing_url": "https://arxiv.org/abs/2610.11941",
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      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7221081866",
  "pdf_url": "https://arxiv.org/pdf/2610.11941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dr4n3kgjb99fm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Number of Hamiltonian Cycles in a Boolean Cube",
  "title_text": "On the Number of Hamiltonian Cycles in a Boolean Cube",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/dr4n3kgjb99fm",
  "venue": "arXiv",
  "versions": []
}