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A309210
Number of main classes of extended self-orthogonal diagonal Latin squares of order n.
5
1, 0, 0, 1, 1, 0, 5, 23, 18865, 33240
OFFSET
1,7
COMMENTS
A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.
A333366(n) <= A329685(n) <= a(n) <= A330391(n). - Eduard I. Vatutin, Jun 07 2020
a(10) >= 33240. - Eduard I. Vatutin, Jul 09 2020
LINKS
Eduard I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
E. Vatutin and A. Belyshev, Enumerating the Orthogonal Diagonal Latin Squares of Small Order for Different Types of Orthogonality, Communications in Computer and Information Science, Vol. 1331, Springer, 2020, pp. 586-597.
Eduard Vatutin and Oleg Zaikin, Classification of Cells Mapping Schemes Related to Orthogonal Diagonal Latin Squares of Small Order, Supercomputing, Russian Supercomputing Days (RuSCDays 2023) Rev. Selected Papers Part II, LCNS Vol. 14389, Springer, Cham, 21-34.
EXAMPLE
The diagonal Latin square
0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 7 9 8 6 3
5 0 1 6 3 9 8 2 4 7
9 3 5 8 2 1 7 4 0 6
4 6 3 5 7 8 0 9 2 1
8 4 6 9 1 3 2 5 7 0
7 8 9 0 6 4 5 1 3 2
2 9 4 7 8 0 3 6 1 5
6 5 7 1 0 2 4 3 9 8
3 7 8 2 9 6 1 0 5 4
has the orthogonal diagonal Latin square
0 1 2 3 4 5 6 7 8 9
3 5 9 8 6 2 0 1 4 7
4 3 8 7 2 1 9 0 5 6
6 9 3 4 8 0 1 2 7 5
7 2 0 1 9 3 5 8 6 4
2 0 1 5 7 6 4 9 3 8
8 6 4 2 0 9 7 5 1 3
1 7 6 0 5 4 8 3 9 2
9 8 5 6 1 7 3 4 2 0
5 4 7 9 3 8 2 6 0 1
from the same main class.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Aug 09 2019
EXTENSIONS
a(9) added by Eduard I. Vatutin, Dec 08 2020
a(10) added by Eduard I. Vatutin, Oleg S. Zaikin, Jan 30 2025
STATUS
approved