The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality.

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My name is David. I live in Texas. I work as a Jack of all Trades for a glass factory. I like building and repairing computers in my spare time. I...

My name is David. I live in Texas. I work as a Jack of all Trades for a glass factory. I like building and repairing computers in my spare time. I...

Processing of the square # 21 completed

Dear participants, processing of the square # 21 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

3 4 5 1 2 0 B 9 A 6 7 8

8 7 6 A 9 B 0 2 1 5 4 3

7 6 8 9 B A 1 0 2 3 5 4

A 9 B 7 6 8 3 5 4 0 2 1

5 3 4 0 1 2 9 A B 7 8 6

B A 9 8 7 6 5 4 3 2 1 0

2 0 1 5 3 4 7 8 6 A B 9

9 B A 6 8 7 4 3 5 1 0 2

6 8 7 B A 9 2 1 0 4 3 5

4 5 3 2 0 1 A B 9 8 6 7

has 1185453085 orthogonal mates, like square square # 8. Presumably a some unknown transformations exist that can convert a square of other main class to this square.

Thank you for project attention, support and donation of CPU time!

28 Jan 2023, 19:39:54 UTC
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Processing of the square # 20 completed

Dear participants, processing of the square # 20 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

3 4 5 1 2 0 B 9 A 6 7 8

9 B A 6 8 7 4 3 5 1 0 2

7 6 8 9 B A 1 0 2 3 5 4

A 9 B 7 6 8 3 5 4 0 2 1

5 3 4 0 1 2 9 A B 7 8 6

B A 9 8 7 6 5 4 3 2 1 0

8 7 6 A 9 B 0 2 1 5 4 3

2 0 1 5 3 4 7 8 6 A B 9

6 8 7 B A 9 2 1 0 4 3 5

4 5 3 2 0 1 A B 9 8 6 7

has 1220317124 orthogonal mates what is equal to number of orthogonal mates of square # 6. We "caught" another square like square # 19 and 17! And that is interesting also.

Thank you for project attention, support and donation of CPU time!

18 Dec 2022, 20:04:04 UTC
· Discuss

Processing of the square # 19 completed

Dear participants, processing of the square # 19 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

2 0 1 5 3 4 7 8 6 A B 9

8 7 6 9 B A 1 0 2 5 4 3

7 6 8 B A 9 2 1 0 3 5 4

B A 9 8 7 6 5 4 3 2 1 0

5 3 4 1 2 0 B 9 A 7 8 6

9 B A 6 8 7 4 3 5 1 0 2

A 9 B 7 6 8 3 5 4 0 2 1

4 5 3 0 1 2 9 A B 8 6 7

3 4 5 2 0 1 A B 9 6 7 8

6 8 7 A 9 B 0 2 1 4 3 5

has 1228403532 orthogonal mates which would puts it on the 4th place of the rating, but another square - #17 already placed on it with equivalent number of orthogonal mates! This is very unexpected because each of the squares is a separate canonical form and cannot be converted into another square by M-transformations. But one square can be transformed into another square by rows and columns permutations. Usually this permutations break the diagonality of squares, but not in this case! Very interesting finding!

Now whole spectra of ODLS-12 globally looks like this (one point is not a single number):

Thank you for participation and donation of CPU Time!

21 Nov 2022, 20:27:05 UTC
· Discuss

Processing of the square # 18 completed

Dear participants, processing of the square # 18 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 6 7 B 9 A

2 0 1 5 3 4 7 8 6 A B 9

6 8 7 9 B A 2 1 0 5 4 3

8 7 6 B A 9 0 2 1 3 5 4

7 6 8 A 9 B 1 0 2 4 3 5

9 B A 8 7 6 5 4 3 0 2 1

A 9 B 6 8 7 4 3 5 2 1 0

B A 9 7 6 8 3 5 4 1 0 2

5 3 4 0 1 2 A B 9 6 7 8

4 5 3 2 0 1 B 9 A 7 8 6

3 4 5 1 2 0 9 A B 8 6 7

has 153240804 orthogonal mates which puts it on the 16th place of the rating which include now 4717 positions. We expected that the smallest number of orthogonal mates would correspond to this square (in comparison to other squares processed in RakeSearch) and now we see that the possible number of orthogonal mates for squares selected for processed in our project lies in the range between hundreds of millions to billions.

Now "high part" of spectra of ODLS-12 looks like this (square # 18 marked by red):

Thank you for participation and donation of CPU Time!

28 Aug 2022, 21:00:45 UTC
· Discuss

Processing of the square # 17 completed

Dear participants, processing of the square # 17 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B

1 2 0 4 5 3 8 9 A B 6 7

2 0 1 5 3 4 A B 6 7 8 9

B 7 9 8 A 6 5 1 3 2 4 0

A 6 8 7 9 B 0 5 1 3 2 4

9 B 7 6 8 A 4 0 5 1 3 2

5 3 4 2 0 1 7 8 9 A B 6

4 5 3 1 2 0 B 6 7 8 9 A

3 4 5 0 1 2 9 A B 6 7 8

6 8 A 9 B 7 1 3 2 4 0 5

7 9 B A 6 8 3 2 4 0 5 1

8 A 6 B 7 9 2 4 0 5 1 3

has 1228403532 orthogonal mates which puts it on the 4th place of the rating among another squares with ~1.2 billion mates!

Now "high part" of spectra of ODLS-12 looks like this (square # 17 marked by red):

Thank you for participation and donation of CPU Time!

20 Jul 2022, 17:24:55 UTC
· Discuss

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©2023 The searchers team, Karelian Research Center of the Russian Academy of Sciences