OFFSET

1,4

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.

a(10) >= 1852743352320000. - Eduard I. Vatutin, Jul 10 2020

LINKS

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 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.

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 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

STATUS

approved