A100540
Total number of Latin 4-dimensional hypercubes (Latin polyhedra) of order n.
Original entry on oeis.org
1, 2, 48, 36972288, 52260618977280
Offset: 1
Toru Ito (t_ito(AT)mue.biglobe.ne.jp), Nov 28 2004
- T. Ito, Method, equipment,program and storage media for producing tables, Publication number JP2004-272104A, Japan Patent Office (in Japanese).
A132206
Total number of Latin 5-dimensional hypercubes (Latin polyhedra) of order n.
Original entry on oeis.org
1, 2, 96, 6268637952000, 2010196727432478720
Offset: 1
Toru Ito (to-itou(AT)ipa.go.jp), Nov 06 2007
4*(4-1)!^5*L5(4) = 6268637952000 where L5(4) = 201538000
- T. Ito, Method, equipment, program and storage media for producing tables, Publication number JP2004-272104A, Japan Patent Office (written in Japanese).
- B. D. McKay and I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22, (2008) 719-736.
- Kenji Ohkuma, Atsuhiro Yamagishi and Toru Ito, Cryptography Research Group Technical report, IT Security Center, Information-Technology Promotion Agency, JAPAN.
Edited by
N. J. A. Sloane, Dec 05 2009 at the suggestion of Vladeta Jovovic
A100539
Number of reduced Latin 4-dimensional hypercubes (Latin polyhedra) of order n.
Original entry on oeis.org
1, 1, 1, 7132, 31503556
Offset: 1
Toru Ito (t_ito(AT)mue.biglobe.ne.jp), Nov 28 2004
- T. Ito, Method, equipment, program and storage media for producing tables, Publication number JP2004-272104A, Japan Patent Office (written in Japanese).
A211214
Number of reduced Latin n-dimensional hypercubes of order 4; labeled n-ary loops of order 4 with fixed identity.
Original entry on oeis.org
1, 1, 4, 64, 7132, 201538000, 432345572694417712, 3987683987354747642922773353963277968, 678469272874899582559986240285280710364867063489779510427038722229750276832
Offset: 0
- T. Ito, Creation Method of Table, Creation Apparatus, Creation Program and Program Storage Medium, U.S. Patent US7228311B2 and Patent application 20040243621, Dec. 2, 2004.
- D. S. Krotov, V. N. Potapov, On the reconstruction of N-quasigroups of order 4 and the upper bounds on their numbers, Proc. Conference devoted to the 90th anniversary of Alexei A. Lyapunov (Novosibirsk, Russia, October 8-11, 2001), 2001.
- D. S. Krotov, V. N. Potapov, n-Ary Quasigroups of Order 4, SIAM J. Discrete Math. 23:2 (2009), 561-570, arXiv: math/0701519.
- B. D. McKay, I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22:2 (2008) 719-736.
- V. N. Potapov, D. S. Krotov, On the number of n-ary quasigroups of finite order, Discrete Mathematics and Applications, 21:5-6 (2011), 575-586, arXiv:0912.5453.
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