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LINKS
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Table of n, a(n) for n=1..9.
S. E. Kochemazov, E. I. Vatutin, O. S. Zaikin, Fast Algorithm for Enumerating Diagonal Latin Squares of Small Order, arXiv:1709.02599 [math.CO], 2017.
S. Kochemazov, O. Zaikin, E. Vatutin, A. Belyshev, Enumerating Diagonal Latin Squares of Order Up to 9, Journal of Integer Sequences. Vol. 23. Iss. 1. 2020. Article 20.1.2.
M. O. Manzuk, N. N. Nikitina, About the number of diagonal Latin squares of order 9 as a one of results of RakeSearch distributed computing project
Eduard I. Vatutin, a(9) value fixed after
E. I. Vatutin, Enumerating the diagonal Latin squares of order 8 using equivalence classes of X-based fillings of diagonals and ESODLS-schemas (in Russian)
E. I. Vatutin, Enumerating the diagonal Latin squares of order 9 using Gerasim@Home volunteer distributed computing project, equivalence classes of X-based fillings of diagonals and ESODLS-schemas (in Russian)
E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, Applying Volunteer and Parallel Computing for Enumerating Diagonal Latin Squares of Order 9, Parallel Computational Technologies. PCT 2017. Communications in Computer and Information Science, vol. 753, pp. 114-129. doi: 10.1007/978-3-319-67035-5_9.
Eduard I. Vatutin, Stepan E. Kochemazov, Oleq S.Zaikin, Maxim O. Manzuk, Natalia N. Nikitina, Vitaly S. Titov, Central symmetry properties for diagonal Latin squares, Problems of Information Technology (2019) No. 2, 3-8.
E. I. Vatutin, O. S. Zaikin, A. D. Zhuravlev, M. O. Manzuk, S. E. Kochemazov and V. S. Titov, Using grid systems for enumerating combinatorial objects on example of diagonal Latin squares, Proceedings of Distributed Computing and grid-technologies in science and education (GRID'16), JINR, Dubna, 2016, pp. 114-115.
Vatutin E. I., Zaikin O. S., Zhuravlev A. D., Manzuk M. O., Kochemazov S. E., Titov V. S., The effect of filling cells order to the rate of generation of diagonal Latin squares, Information-measuring and diagnosing control systems (Diagnostics - 2016). Kursk: SWSU, 2016. pp. 33-39 (in Russian).
E. I. Vatutin, V. S. Titov, O. S. Zaikin, S. E. Kochemazov, S. U. Valyaev, A. D. Zhuravlev, M. O. Manzuk, Using grid systems for enumerating combinatorial objects with example of diagonal Latin squares, Information technologies and mathematical modeling of systems (2016), pp. 154-157, (in Russian).
Vatutin E.I., Zaikin O.S., Zhuravlev A.D., Manzyuk M.O., Kochemazov S.E., Titov V.S., Using grid systems for enumerating combinatorial objects on example of diagonal Latin squares, CEUR Workshop proceedings. Selected Papers of the 7th International Conference Distributed Computing and Grid-technologies in Science and Education. 2017. Vol. 1787. pp. 486-490. urn:nbn:de:0074-1787-5.
Index entries for sequences related to Latin squares and rectangles
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EXAMPLE
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The a(4) = 2 diagonal Latin squares are:
0 1 2 3 0 1 2 3
2 3 0 1 3 2 1 0
3 2 1 0 1 0 3 2
1 0 3 2 2 3 0 1
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The a(5) = 8 diagonal Latin squares are:
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
1 3 4 2 0 1 4 3 0 2 2 3 4 0 1 2 4 1 0 3
4 2 1 0 3 3 2 1 4 0 4 0 1 2 3 4 0 3 2 1
2 0 3 4 1 4 3 0 2 1 1 2 3 4 0 3 2 4 1 0
3 4 0 1 2 2 0 4 1 3 3 4 0 1 2 1 3 0 4 2
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0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
3 4 0 1 2 3 4 1 2 0 4 2 0 1 3 4 2 3 0 1
1 2 3 4 0 4 2 3 0 1 1 4 3 2 0 3 4 1 2 0
4 0 1 2 3 2 0 4 1 3 3 0 1 4 2 1 3 0 4 2
2 3 4 0 1 1 3 0 4 2 2 3 4 0 1 2 0 4 1 3
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