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On the reconstruction of n-quasigroups of order $4$ and upper bounds on their number

  • Denis S. Krotov
  • Vladimir N. Potapov
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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 3n+122n+1 of that number is established.

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Cite

BibTeXRIS
BibTeX
@misc{krotov2026reconstruction,
  title = {{On the reconstruction of $n$-quasigroups of order $4$ and upper bounds on their number}},
  author = {Denis S. Krotov and Vladimir N. Potapov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03116},
  eprint = {2609.03116},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03116},
}
RIS
TY  - UNPB
TI  - On the reconstruction of n-quasigroups of order $4$ and upper bounds on their number
AU  - Denis S. Krotov
AU  - Vladimir N. Potapov
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03116
UR  - https://arxiv.org/abs/2609.03116
AB  - (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+12^2^n+1 of that number is established.
ER  -