A309210
Number of main classes of extended self-orthogonal diagonal Latin squares of order n.
Original entry on oeis.org
1, 0, 0, 1, 1, 0, 5, 23, 18865, 33240
Offset: 1
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.
- E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian)
- E. I. Vatutin, About the lower bound of number of ESODLS of order 10 (in RUssian).
- E. I. Vatutin, List of all main classes of extended self-orthogonal diagonal Latin squares of orders 1-8.
- E. I. Vatutin, List of all main classes of extended self-orthogonal diagonal Latin squares of order 9.
- E. I. Vatutin, List of all main classes of extended self-orthogonal diagonal Latin squares of order 10.
- 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 I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch (in Russian).
- 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.
- Index entries for sequences related to Latin squares and rectangles
A329685
Number of main classes of self-orthogonal diagonal Latin squares of order n.
Original entry on oeis.org
1, 0, 0, 1, 1, 0, 2, 8, 470, 30502
Offset: 1
0 1 2 3 4 5 6 7 8 9
5 2 0 9 7 8 1 4 6 3
9 5 7 1 8 6 4 3 0 2
7 8 6 4 9 2 5 1 3 0
8 9 5 0 3 4 2 6 7 1
3 6 9 5 2 1 7 0 4 8
4 3 1 7 6 0 8 2 9 5
6 7 8 2 5 3 0 9 1 4
2 0 4 6 1 9 3 8 5 7
1 4 3 8 0 7 9 5 2 6
- A. D. Belyshev, List of 30502 essentially distinct self-orthogonal diagonal Latin squares of order 10
- E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian).
- E. I. Vatutin, About the number of main classes for SODLS of order 9 (in Russian).
- E. I. Vatutin, About the number of SODLS of order 10 (in Russian).
- E. I. Vatutin, List of all main classes of self-orthogonal diagonal Latin squares of orders 1-10.
- E. 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. I. Vatutin and A. D. Belyshev, About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10. High-performance computing systems and technologies. Vol. 4. No. 1. 2020. pp. 58-63. (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 I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch (in Russian).
- Index entries for sequences related to Latin squares and rectangles
A333367
Number of doubly self-orthogonal diagonal Latin squares of order n with the first row in ascending order.
Original entry on oeis.org
1, 0, 0, 2, 4, 0, 64, 1152, 28608, 0
Offset: 1
0 1 2 3 4 5 6 7 8
2 4 3 0 7 6 8 1 5
4 6 7 1 8 2 3 5 0
8 3 5 6 0 7 1 2 4
7 8 1 4 5 3 0 6 2
3 7 0 2 1 8 5 4 6
1 5 4 7 6 0 2 8 3
5 0 6 8 2 1 4 3 7
6 2 8 5 3 4 7 0 1
- R. Lu, S. Liu, and J. Zhang, Searching for Doubly Self-orthogonal Latin Squares. Lecture Notes in Computer Science 6876 (2011), 538-545.
- E. I. Vatutin, About the number of DSODLS of orders 1-10 (in Russian).
- E. I. Vatutin, List of all main classes of doubly self-orthogonal diagonal Latin squares of orders 1-10.
- E. 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. I. Vatutin and A. D. Belyshev, About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10. High-performance computing systems and technologies. Vol. 4. No. 1. 2020. pp. 58-63. (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.
- Index entries for sequences related to Latin squares and rectangles.
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