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arXiv · 2609.03116

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 $3^{n+1}2^{2^n+1}$ of that number is established.

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Denis S. Krotov, Vladimir N. Potapov. 2026-09-02. On the reconstruction of $n$-quasigroups of order $4$ and upper bounds on their number. https://arxiv.org/abs/2609.03116

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