[Natalia Makarova]

Dear colleagues!

BOINC project for ODLS of order 10 started

https://boinc.progger.info/odlk/

Join the project!
Support the project with your computers.

Thank you.

[Natalia Makarova]

A database of unique CF DLS of order 10 having orthogonal DLS
as of March 31, 2017 (38711 unique CF)

https://yadi.sk/d/2qQ5B7dS3GYEgD

[Natalia Makarova]

Dear colleagues!

You can take part in the discussion of the BOINC-project Stop@home here
http://stop.inferia.ru/forum_forum.php?id=3

You can also take part in the calculations.

[Natalia Makarova]

Here a database, obtained in my project (before the BOINC-project)
http://forum.boinc.ru/default.aspx?g=posts&m=86353#post86353

Let me remind you:
my project “Symmetrical tuples of consecutive primes” started in forum dxdy.ru (Russia, 9 February 2015)
http://dxdy.ru/topic93581.html

[Natalia Makarova]

Dear colleagues!

The project «Symmetrical tuples of consecutive primes» changed the name and address.
See here
http://forum.boinc.ru/default.aspx?g=posts&m=86435#post86435

The new address of the project
http://stop.inferia.ru

The new name of the project
Stop@home

• Questa risposta è stata modificata 7 anni, 2 mesi fa da Natalia Makarova.

[Natalia Makarova]

Dear colleagues!

You can participate in the discussion of the project at a forum in Russia
http://mathhelpplanet.com/viewtopic.php?f=57&t=52906

You can write messages in English.

[Natalia Makarova]

Dear colleagues!

The project “Symmetrical tuples of consecutive primes” is in testing for BOINC
http://inferia.ru

I invite everyone to participate!

[Natalia Makarova]

My colleagues and I continue to be ODLS database.
Here you can view a database containing 5184 ODLS

https://yadi.sk/d/SEjRxCkH3B3uYv

One of the new solution – a group of four pairs ODLS

Square A

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

Square B

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

Square C

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

Square D

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

Square E

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

Orthogonal pairs: A – B, A – C, A – D, A – E.

I invite everyone to take part in the project!

• Questa risposta è stata modificata 7 anni, 3 mesi fa da Natalia Makarova.

[Natalia Makarova]

Dear colleagues!

I offer you a database ODLS of order 10

https://yadi.sk/d/vA2ttrr_32dfWk

At present, the database contains 4022 ODLS.

Once again I invite you to take part in the preparation of the database.

[Natalia Makarova]

My project
Orthogonal Diagonal Latin squares of order 10

Discussion forum on the project, see Math Help Planet
http://mathhelpplanet.com/viewtopic.php?f=57&t=46638

Today we have a database – 3984 of orthogonal DLS of order 10.
Example group of two pairs of orthogonal DLS

A

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

B

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

C

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

Orthogonal pairs DLS: A – B, A – C.

I invite everyone to take part in the discussion of the problem. You can write your message in English.

Dear colleagues!

Please take part in my project.
You get a job, such as

start

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

end

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

Record the start-square in start.txt file, record the end-square in end.txt file.
Run the batch file run.bat

@echo off
color 0A
for /l %%i in (1,1,100) do (
GenInterval3.exe < interval.txt
lat03c_mod.exe < vvod.txt
copy /b rez.txt+o_output.txt rez.txt
del output.txt
echo  %%i Complite
)
pause
exit

After executing a batch file, you will see the results in rez.txt file if the results are found.
Please let me know if you are ready to take part in the project. You need to get a job and a batch file.

My e-mail
[email protected]

[Natalia Makarova]

Dear colleagues!

I bring to your attention an article
“Systems of N mutually orthogonal diagonal Latin squares of order 10 with a complete orthogonality (N-1) pairs”
https://yadi.sk/i/S417t0IpwnP6r

Please send feedback to me at [email protected]

[Natalia Makarova]

I found a new unique group of two pairs orthogonal diagonal latin squares of order 10

Square A

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

Square B

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

Square C

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

The group found a random generation of DLS with my program.
Searching orthogonal squares used program S. Belyaev.

• Questa risposta è stata modificata 7 anni, 9 mesi fa da Natalia Makarova.
• Questa risposta è stata modificata 7 anni, 9 mesi fa da Natalia Makarova.
• Questa risposta è stata modificata 7 anni, 9 mesi fa da primesmagicgames.

[Natalia Makarova]

Systems of four LS of order 10 with partial orthogonality

Example

Square A

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

Square B

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

Square C

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

Square D

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

Orthogonal pairs: A – B, A – C, A – D, partially orthogonal pairs: B – C, B – D, C – D.

B – C

00  11  22  33  44  55  66  77  88  99 
47  83  76  52  01  94  39  60  25  18 
15  07  43  61  58  80  72  29  96  34 
73  32  68  20  19  46  91  05  54  87 
59  76  31  18  82  03  25  94  67  40 
36  24  85  09  97  61  10  58  43  72 
98  65  19  87  23  32  54  41  70  06 
62  49  50  94  76  17  08  83  31  25 
84  58  97  75  30  29  43  16  02  61 
21  90  04  46  65  78  87  32  19  53

00 01 02 03 04 05 06 07 08 09 10 11 15 16 17 18 19 20 21 22 23 24 25 29 30 31 32 33 34 36 39 40 41 43 44 46 47 49 50 52 53 54 55 58 59 60 61 62 65 66 67 68 70 72 73 75 76 77 78 80 82 83 84 85 87 88 90 91 94 96 97 98 99
The number of unique ordered pairs: U = 73

B – D

00  11  22  33  44  55  66  77  88  99 
48  82  75  59  06  97  34  63  20  11 
12  08  40  65  53  89  77  24  91  36 
74  39  67  26  10  41  98  02  55  83 
51  70  33  17  85  04  29  96  62  48 
37  23  84  01  99  68  12  50  46  75 
95  66  18  82  21  30  53  49  74  07 
63  47  51  90  72  16  05  88  39  24 
89  54  96  78  37  22  41  15  03  60
26  95  09  44  68  73  80  31  17  52

00 01 02 03 04 05 06 07 08 09 10 11 12 15 16 17 18 20 21 22 23 24 26 29 30 31 33 34 36 37 39 40 41 44 46 47 48 49 50 51 52 53 54 55 59 60 62 63 65 66 67 68 70 72 73 74 75 77 78 80 82 83 84 85 88 89 90 91 95 96 97 98 99
The number of unique ordered pairs: U = 73

C – D

00  11  22  33  44  55  66  77  88  99 
78  32  65  29  16  47  94  03  50  81 
52  78  30  15  83  09  27  94  61  46 
34  29  87  06  90  61  18  52  45  73 
91  60  13  87  25  34  59  46  72  08 
67  43  54  91  79  18  02  80  36  25 
85  56  98  72  31  20  43  19  04  67 
23  97  01  40  62  76  85  38  19  54 
49  84  76  58  07  92  31  65  23  10 
16  05  49  64  58  83  70  21  97  32

00 01 02 03 04 05 06 07 08 09 10 11 13 15 16 18 19 20 21 22 23 25 27 29 30 31 32 33 34 36 38 40 43 44 45 46 47 49 50 52 54 55 56 58 59 60 61 62 64 65 66 67 70 72 73 76 77 78 79 80 81 83 84 85 87 88 90 91 92 94 97 98 99
The number of unique ordered pairs: U = 73

The number of unique ordered pairs simultaneously for B – C, B – D, C – D: R=55

00 47 15 73 59 36 98 62 84 21 11 83 07 65 49 90 22 31 85 50 97 04 33 52 20 18 09 46 44 01 23 30 55 80 03 29 78 66 72 91 10 54 08 77 60 05 16 88 67 70 02 99 34 40 06

We call R value – characteristic orthogonality of system with partial orthogonality.
I was unable to find a system of four LS of order 10 with partial orthogonality, for which R> 55.

[Natalia Makarova]

I and my colleagues found the group MOLS of three LS which incomplete orthogonality with the orthogonal coefficient 86.

Square A (DLK)

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

Square B

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

Square C

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

[Natalia Makarova]

My colleagues found the group MOLS of three LS which incomplete orthogonality with the orthogonal coefficient 85

Square A from Parker

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

Square B

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

Square C

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

[Autore]

Post