Abstract
The asymptotic form of the number of n-quasigroups of order 4 is \(3^{n + 1} 2^{2^n + 1} (1 + o(1))\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belousov V. D., n-Ary Quasigroups [in Russian], Shtiintsa, Kishinev (1972).
Krotov D. S. and Potapov V. N., “On the reconstruction of n-quasigroups of order 4 and the upper bounds on their number,” in: Proceedings of the Conference Devoted to the 90th Anniversary of Alexei A. Lyapunov, Novosibirsk, Russia, October 8–11, 2001, pp. 323–327 [http://www.sbras.ru/ws/Lyap2001/2363].
Krotov D. S., “On decomposition of (n, 4n−1, 2)4 MDS codes and double-codes,” in: Proceedings of Eighth International Workshop on Algebraic and Combinatorial Coding Theory (ACCT-VIII), Sept. 8–14, 2002, Tsarskoe Selo, Russia, pp. 168–171.
Krotov D. S., “On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4,” arXiv.orgeprint math.CO/0509358, 2005. Available at http://arxiv.org/abs/math/0509358 (submitted to Discrete Mathematics).
Krotov D. S., “Lower estimates for the number of m-quasigroups of order 4 and for the number of perfect binary codes,” Diskret. Anal. Issled. Oper. Ser. 1, 7, No. 2, 47–53 (2000).
Mullen G. L. and Weber R. E., “Latin cubes of order ≤ 5,” Discrete Math., 32, No. 3, 291–298 (1988).
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2006 Potapov V. N. and Krotov D. S.
The first author was supported by the Russian Foundation for Basic Research (Grant 05-01-00364).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 4, pp. 873–887, July–August, 2006.
Rights and permissions
About this article
Cite this article
Potapov, V.N., Krotov, D.S. Asymptotics for the number of n-quasigroups of order 4. Sib Math J 47, 720–731 (2006). https://doi.org/10.1007/s11202-006-0083-9
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11202-006-0083-9