Posts by Tomas Brada

1) Message boards : Science : ОДЛК для порядков n>10 (Message 5936)
Posted 3 Jul 2020 by Tomas Brada
Post:
I confirm, there are no orthogonal pairs within the 41644 DLK orthogonal to DrdVfwmF2ghiNUw45W9NmZr4iDgJwV49.
2) Message boards : Science : ОДЛК для порядков n>10 (Message 5930)
Posted 3 Jul 2020 by Tomas Brada
Post:
Here I release the program: https://boinc.tbrada.eu/download/dlkconv.exe
dlkconv.exe: (input-spec) [input] [(output-spec) [output]]
** Diagonal Latin Square converter and normalizer **
input-spec: Endoded/compressed (e), Alphanumeric (a), stdin (s) File (f).
 Encoded input can be passed immediately on command line.
 Othervise a NxN matrix of decimal numbers, or Alphanumeric (a) must be
 passed via stdin or file. Multiple orders (N) may be mixed on input.
 Empty lines and (one) trailing spaces are ignored.
output-spec: (e)(a)(f), stdout (s), Compact (c), Diagonal (d)
 LS normalized on first row are written to stdout by default.
 Space between output squares are ommited in Compact (c) mode.
 With (d), output matrix is normalized on main diagonal.
Example dlkconv.exe e 7yPG4 dc -- decode 7yPG4 and normalize diagonal
Author: Tomas Brada (GPL)
3) Message boards : Science : ОДЛК для порядков n>10 (Message 5927)
Posted 2 Jul 2020 by Tomas Brada
Post:
Dear Natalia. I wrote routines to convert the squares between different formats, now just put it into a program and compile it on windows. Then I will release.
4) Message boards : Science : ОДЛК для порядков n>10 (Message 5919)
Posted 1 Jul 2020 by Tomas Brada
Post:
I created a program to compress any size diagonal latin square, similar to namechdlk10. Of course, needs de-compressor too.
Example:
DrdVfwmF2ghiNUw45W9NmZr4iDgJwV49
0 1 2 3 4 5 6 7 8 9 10 11 
3 6 1 4 11 2 9 0 7 10 5 8 
1 4 11 2 5 8 3 6 9 0 7 10 
2 3 4 5 10 11 0 1 6 7 8 9 
11 10 5 0 7 6 1 8 3 2 9 4 
8 5 6 11 0 9 10 3 4 1 2 7 
6 11 0 9 2 7 8 5 10 3 4 1 
5 0 7 6 9 4 11 10 1 8 3 2 
10 7 8 1 6 3 4 9 2 11 0 5 
9 8 3 10 1 0 7 2 5 4 11 6 
7 2 9 8 3 10 5 4 11 6 1 0 
4 9 10 7 8 1 2 11 0 5 6 3
5) Message boards : Science : ОДЛК для порядков n>10 (Message 5912)
Posted 30 Jun 2020 by Tomas Brada
Post:
In my project, I have a DLK10 with 1212 transversals.

Вы имеете в виду диагональные трансверсали или общие трансверсали?

After checking my notes, those are unfortunately general transverses.
6) Message boards : Science : ОДЛК для порядков n>10 (Message 5910)
Posted 30 Jun 2020 by Tomas Brada
Post: 
width: 19 isLK isDLK
0 9 1 6 8 7 3 5 4 17 18 14 13 15 11 10 12 2 16    
2 1 9 8 7 6 5 4 3 16 13 18 14 10 15 11 0 12 17    
1 0 2 9 6 8 4 3 5 15 14 13 18 11 10 7 17 16 12    
6 8 7 3 9 4 0 2 1 14 12 17 16 18 5 13 15 11 10    
8 7 6 5 4 9 2 1 0 13 16 12 17 3 18 14 10 15 11    
7 6 8 4 3 5 9 0 2 12 17 16 1 14 13 18 11 10 15    
3 5 4 0 2 1 6 9 7 11 15 8 10 12 17 16 18 14 13    
5 4 3 2 1 0 8 7 9 10 6 15 11 16 12 17 13 18 14    
9 3 5 1 0 2 7 6 8 18 11 10 15 17 16 12 14 13 4    
18 17 16 15 14 13 12 11 10 9 5 1 6 2 7 3 8 4 0 
14 15 13 17 18 16 11 12 6 1 10 9 8 0 4 2 3 7 5    
13 14 15 16 17 18 10 8 12 6 1 11 9 4 2 0 7 5 3 
15 13 14 18 16 17 1 10 11 2 8 6 12 9 0 4 5 3 7 
11 12 10 14 15 3 17 18 16 7 0 4 2 13 9 5 6 1 8 
10 11 12 13 5 15 16 17 18 3 4 2 0 7 14 9 1 8 6 
12 10 11 7 13 14 18 16 17 8 2 0 4 5 3 15 9 6 1 
17 18 0 11 12 10 14 15 13 4 3 7 5 6 1 8 16 9 2 
16 2 18 10 11 12 13 14 15 0 7 5 3 1 8 6 4 17 9 
4 16 17 12 10 11 15 13 14 5 9 3 7 8 6 1 2 0 18 
init_trans(19) used 1181 nodes
num_trans: 631935677
time: 20m 35.8s
7) Message boards : Science : ОДЛК для порядков n>10 (Message 5909)
Posted 30 Jun 2020 by Tomas Brada
Post: 
width: 16 isLK isDLK
0 14 1 7 2 4 3 5 13 11 12 10 15 9 6 8 
15 1 6 0 5 3 4 2 10 12 11 13 8 14 9 7 
3 5 2 12 1 7 0 6 14 8 15 9 4 10 13 11 
4 2 13 3 6 0 7 1 9 15 8 14 11 5 10 12 
6 0 7 1 4 10 5 3 11 13 2 12 9 15 8 14 
1 7 0 6 11 5 2 4 12 10 13 3 14 8 15 9 
5 3 4 2 7 1 6 8 0 14 9 15 10 12 11 13 
2 4 3 5 0 6 9 7 15 1 14 8 13 11 12 10 
13 11 12 10 15 9 14 0 8 6 1 7 2 4 3 5 
10 12 11 13 8 14 1 15 7 9 6 0 5 3 4 2 
14 8 15 9 12 2 13 11 3 5 10 4 1 7 0 6 
9 15 8 14 3 13 10 12 4 2 5 11 6 0 7 1 
11 13 10 4 9 15 8 14 6 0 7 1 12 2 5 3 
12 10 5 11 14 8 15 9 1 7 0 6 3 13 2 4 
8 6 9 15 10 12 11 13 5 3 4 2 7 1 14 0 
7 9 14 8 13 11 12 10 2 4 3 5 0 6 1 15 
init_trans(16) used 851 nodes
num_trans: 15456144
time: 10.5s
8) Message boards : Science : ОДЛК для порядков n>10 (Message 5905)
Posted 30 Jun 2020 by Tomas Brada
Post:
Number of transversals.
In my project, I have a DLK10 with 1212 transversals.
But A287644 a(10) >= 5504 from Parker and Brown.
width: 15 isLK isDLK
0 7 8 9 6 13 10 4 3 5 12 2 11 14 1 
4 1 7 0 8 14 12 5 6 11 3 10 13 2 9 
14 5 2 7 1 0 13 6 10 4 9 12 3 8 11 
9 13 6 3 7 2 1 14 5 8 11 4 0 10 12 
6 8 12 14 4 7 3 13 0 10 5 1 9 11 2 
1 14 0 11 13 5 7 12 9 6 2 8 10 3 4 
8 2 13 1 10 12 6 11 14 3 0 9 4 5 7 
11 10 9 8 0 1 2 7 12 13 14 6 5 4 3 
7 9 10 5 14 11 0 3 8 2 4 13 1 12 6 
10 11 4 6 12 8 5 2 7 9 1 3 14 0 13 
12 3 5 13 9 4 14 1 11 7 10 0 2 6 8 
2 4 14 10 3 6 9 0 13 12 7 11 8 1 5 
3 6 11 2 5 10 4 8 1 14 13 7 12 9 0 
5 12 1 4 11 3 8 9 2 0 6 14 7 13 10 
13 0 3 12 2 9 11 10 4 1 8 5 6 7 14 
init_trans(15) used 753 nodes
num_trans: 305408
time: <1s

width: 16 isLK isDLK
0 7 8 6 9 10 13 14 5 3 4 2 15 12 11 1 
5 1 7 8 6 9 12 13 15 4 3 14 11 10 2 0 
4 15 2 7 8 6 11 12 14 5 13 10 0 3 1 9 
12 5 14 3 7 8 10 11 13 15 0 1 4 2 9 6 
1 11 15 13 4 7 0 10 12 14 2 5 3 9 6 8 
3 2 10 14 12 5 1 0 11 13 15 4 9 6 8 7 
10 0 1 2 3 4 6 9 7 8 11 12 13 14 15 5 
11 10 0 1 2 3 8 7 9 6 12 13 14 15 5 4 
13 12 11 10 0 1 9 6 8 7 14 15 5 4 3 2 
2 3 4 5 15 14 7 8 6 9 1 0 10 11 12 13 
7 8 6 9 11 0 14 15 4 2 10 3 1 5 13 12 
8 6 9 12 10 13 15 5 3 1 7 11 2 0 4 14 
6 9 13 11 14 15 5 4 2 0 8 7 12 1 10 3 
9 14 12 15 5 2 4 3 1 10 6 8 7 13 0 11 
15 13 5 4 1 12 3 2 0 11 9 6 8 7 14 10 
14 4 3 0 13 11 2 1 10 12 5 9 6 8 7 15 
init_trans(16) used 851 nodes
num_trans: 1879316
time: 2.3s

width: 17 isLK isDLK
0 8 9 10 12 15 13 6 5 2 4 7 3 11 16 14 1 
3 1 8 0 9 11 14 12 6 5 16 4 10 15 13 2 7 
6 4 2 8 1 0 10 13 7 15 5 9 14 12 3 16 11 
14 7 5 3 8 2 1 9 16 6 0 13 11 4 15 10 12 
7 13 16 6 4 8 3 2 15 1 12 10 5 14 9 11 0 
2 16 12 15 7 5 8 4 14 11 9 6 13 0 10 1 3 
10 3 15 11 14 16 6 8 13 0 7 12 1 9 2 4 5 
1 9 4 14 10 13 15 7 12 16 11 2 0 3 5 6 8 
12 11 10 9 0 1 2 3 8 13 14 15 16 7 6 5 4 
8 10 11 13 16 14 5 0 4 9 1 3 6 2 12 7 15 
11 12 14 7 15 4 9 16 3 8 10 0 2 5 1 13 6 
13 15 6 16 3 10 7 5 2 12 8 11 9 1 4 0 14 
16 5 7 2 11 6 4 15 1 14 13 8 12 10 0 3 9 
4 6 1 12 5 3 16 10 0 7 15 14 8 13 11 9 2 
5 0 13 4 2 7 11 1 9 3 6 16 15 8 14 12 10 
9 14 3 1 6 12 0 11 10 4 2 5 7 16 8 15 13 
15 2 0 5 13 9 12 14 11 10 3 1 4 6 7 8 16 
init_trans(17) used 955 nodes
num_trans: 12102527
time: 21.4s

width: 18 isLK isDLK
0 4 7 10 8 9 1 11 3 12 2 6 13 15 17 5 14 16 
17 1 5 7 10 8 9 0 4 11 3 12 14 16 6 13 15 2 
11 16 2 6 7 10 8 1 5 0 4 13 15 17 12 14 3 9 
12 0 15 3 17 7 10 2 6 1 5 14 16 11 13 4 9 8 
13 11 1 14 4 16 7 3 17 2 6 15 0 12 5 9 8 10 
14 12 0 2 13 5 15 4 16 3 17 1 11 6 9 8 10 7 
2 13 11 1 3 12 6 5 15 4 16 0 17 9 8 10 7 14 
16 15 14 13 12 11 0 7 10 8 9 17 6 5 4 3 2 1 
5 6 17 16 15 14 13 9 8 10 7 4 3 2 1 0 11 12 
4 5 6 17 16 15 14 10 7 9 8 3 2 1 0 11 12 13 
6 17 16 15 14 13 12 8 9 7 10 5 4 3 2 1 0 11 
3 7 10 8 9 0 17 12 2 13 1 11 5 14 16 6 4 15 
7 10 8 9 11 6 16 13 1 14 0 2 12 4 15 17 5 3 
10 8 9 12 5 17 2 14 0 15 11 7 1 13 3 16 6 4 
8 9 13 4 6 1 3 15 11 16 12 10 7 0 14 2 17 5 
9 14 3 5 0 2 4 16 12 17 13 8 10 7 11 15 1 6 
15 2 4 11 1 3 5 17 13 6 14 9 8 10 7 12 16 0 
1 3 12 0 2 4 11 6 14 5 15 16 9 8 10 7 13 17 
init_trans(18) used 1065 nodes
num_trans: 82602438
time: 2m 57.4s
9) Message boards : Science : ОДЛК для порядков n>10 (Message 5904)
Posted 30 Jun 2020 by Tomas Brada
Post:
ДЛК 13-го порядка
0 12 11 7 10 4 8 2 3 5 6 9 1 
3 1 12 0 8 11 9 4 6 7 10 2 5 
5 4 2 12 1 9 10 7 8 11 3 6 0 
8 6 5 3 12 2 11 9 0 4 7 1 10 
10 9 7 6 4 12 0 1 5 8 2 11 3 
2 11 10 8 7 5 1 6 9 3 0 4 12 
1 2 3 4 5 6 12 0 11 10 9 8 7 
12 10 6 9 3 0 7 11 1 2 4 5 8 
9 5 8 2 11 7 6 12 10 0 1 3 4 
4 7 1 10 6 3 5 8 12 9 11 0 2 
6 0 9 5 2 1 4 3 7 12 8 10 11 
11 8 4 1 0 10 3 5 2 6 12 7 9 
7 3 0 11 9 8 2 10 4 1 5 12 6

I confirm that this square has 9840 d-transverses and my porogram found 45 orthogonal mates. It took just over two hours on my PC. First two are:
8 7 0 1 6 9 3 10 5 11 12 4 2 
9 0 4 6 10 3 8 11 1 12 2 5 7 
3 6 11 10 1 5 9 8 0 4 7 2 12 
2 10 5 4 8 6 1 7 3 0 9 12 11 
12 9 6 0 5 11 2 3 4 7 8 10 1 
4 12 10 9 7 1 5 6 11 2 0 8 3 
10 2 8 7 0 4 12 9 6 3 1 11 5 
6 5 7 12 11 10 0 2 8 1 3 9 4 
0 8 12 3 9 2 11 1 7 5 4 6 10 
1 4 9 8 3 12 6 5 2 10 11 7 0 
5 11 3 2 12 7 4 0 10 9 6 1 8 
7 1 2 11 4 0 10 12 9 8 5 3 6 
11 3 1 5 2 8 7 4 12 6 10 0 9 

3 6 0 8 2 4 7 5 9 10 11 1 12 
12 0 11 4 5 6 3 1 2 9 8 10 7 
4 11 2 3 7 8 1 0 10 5 6 12 9 
9 5 6 7 10 12 2 4 8 0 1 3 11 
0 7 12 10 9 2 5 11 3 6 4 8 1 
8 12 4 11 3 1 9 7 5 2 10 6 0 
1 3 5 2 11 9 8 6 7 12 0 4 10 
5 9 1 12 0 11 6 10 4 7 3 2 8 
10 8 3 9 4 7 0 12 6 1 2 11 5 
7 4 10 5 8 3 12 2 1 11 9 0 6 
6 2 9 0 1 5 10 8 11 4 12 7 3 
11 1 8 6 12 10 4 9 0 3 7 5 2 
2 10 7 1 6 0 11 3 12 8 5 9 4
10) Message boards : Science : ОДЛК для порядков n>10 (Message 5888)
Posted 29 Jun 2020 by Tomas Brada
Post:
Example for method 1 on DLK12.
In this one, there are 292 rows in the smallest column. Solving just first 10 of them gives the following distribution of solutions:
l(1) 1 / 292 r304 s2  
l(1) 2 / 292 r592 s0  
l(1) 3 / 292 r916 s6  
l(1) 4 / 292 r928 s144
l(1) 5 / 292 r940 s17  
l(1) 6 / 292 r1552 s10
l(1) 7 / 292 r1564 s13                    
l(1) 8 / 292 r1576 s16
l(1) 9 / 292 r1588 s10

(number of solutions is the last number)
Stopping after first solution is also possible.
11) Message boards : Science : ОДЛК для порядков n>10 (Message 5885)
Posted 29 Jun 2020 by Tomas Brada
Post:
У меня есть такая идея (возможно, не совсем правильная): нельзя ли ограничить количество трансверсалей, а не задействовать их сразу все?
Вот в программе Белышева заложен некоторый максимум количества трансверсалей; хорошо, пусть для трансверсалей, найденных до этого максимума, и поищутся ортогональные ДЛК. Так нельзя поискать?
Нельзя ли искать ортогональные ДЛК только для этого множества диагональных трансверсалей?

Yes. This is possible. But it will most likely not find a solution.
There are actually two ways:

1) find all transversals, build the sparse matrix, and then limit how far the algorithm backtracks.
This has a good chance of finding a solution.

2) terminate the transversal search after X transversals found, but proceed next step as normal.
This has smaller chance of finding a solution, but avoids running out of memory.
12) Message boards : Science : ОДЛК для порядков n>10 (Message 5883)
Posted 29 Jun 2020 by Tomas Brada
Post:
I fixed my program and verified that the DLK11 has right number of d-transversals and co-squares.
Then I tried a DLK13, but I could not find a good input square, can you give me an example?
Now I am checking DLK14 (this one), but the sparse matrix has over 5 million nodes, it is going to take a long time, I do not know how long.
One DLK16 has 1879316 transversals, which yields over 30 million nodes in sparse matrix and 116138 rows in the smallest column. Huge numbers.
I definitely can not do DLK 26, it has more transversals than fit in my computer memory, and even if it did fit, is would run for a century.
We can try to just count the number of transversals, to provide lower bound to the oeis sequence.
13) Message boards : Science : ОДЛК для порядков n>10 (Message 5881)
Posted 29 Jun 2020 by Tomas Brada
Post:
Solving squares with large number of transversals is hard. This might help:
https://janmagnet.files.wordpress.com/2008/07/decs-report.pdf
Unfortunately, the code is no longer accessible in the direct way. But when I find it, it could run under my boinc project.
14) Message boards : Science : ОДЛК для порядков n>10 (Message 5877)
Posted 28 Jun 2020 by Tomas Brada
Post:
Sorry, I did not get the archive. Please send it to xbrada17@stud.fit.vutbr.cz I am sorry for inconvenience!
And I found that my program only work for DLK of even n (10, 12, etc). I made a mistake for the central element, where the diagonals cross.
15) Message boards : Science : ОДЛК для порядков n>10 (Message 5858)
Posted 27 Jun 2020 by Tomas Brada
Post:
Hello Natalia!
I am trying my luck at programming for DLK n>10. And I made a multi-threaded program similar to ortogon_u (i do not have a source). I do not know if correct yet.
DLK 12 from message
square:
0 1 2 3 4 5 6 7 8 9 10 11 
4 2 6 0 3 10 1 8 11 5 9 7 
8 0 4 10 5 2 9 6 1 7 11 3 
10 3 0 5 9 4 7 2 6 11 8 1 
5 4 3 2 10 11 0 1 9 8 7 6 
2 5 10 7 0 3 8 11 4 1 6 9 
6 7 8 9 1 0 11 10 2 3 4 5 
1 8 11 6 2 7 4 9 5 0 3 10 
9 6 1 4 11 8 3 0 7 10 5 2 
7 9 5 11 8 1 10 3 0 6 2 4 
11 10 9 8 7 6 5 4 3 2 1 0 
3 11 7 1 6 9 2 5 10 4 0 8 
isLK: 1
isDLK: 1
width: 12                
init_trans(12) used 495 nodes
num_trans: 5718          
init_disjoint(12) used 145 heads and 68761 nodes
dance_mt: using 16 threads for 292 rows in column 42
l(1) 292 / 292   
isODLK: 2199 orthogonal mates
57 seconds

Appears to be OK!

DLK 11 No3 from message
width: 11
0 1 2 3 4 5 6 7 8 9 10 
3 4 5 6 7 8 9 10 0 1 2 
6 7 8 9 10 0 1 2 3 4 5 
9 10 0 1 2 3 4 5 6 7 8 
1 2 3 4 5 6 7 8 9 10 0 
4 5 6 7 8 9 10 0 1 2 3 
7 8 9 10 0 1 2 3 4 5 6 
10 0 1 2 3 4 5 6 7 8 9 
2 3 4 5 6 7 8 9 10 0 1 
5 6 7 8 9 10 0 1 2 3 4 
8 9 10 0 1 2 3 4 5 6 7
isLK: 1
isDLK: 1
init_trans(11) used 420 nodes
num_trans: 4700
init_disjoint(11) used 122 heads and 51822 nodes
dance_mt: using 16 threads for 396 rows in column 7
l(1) 396 / 396                                                     
isODLK: 0 orthogonal mates
time: 3m 2s

Is this correct Where error?

Checking more squares...
16) Message boards : Number crunching : About Stop@home project (Message 5584)
Posted 12 May 2020 by Tomas Brada
Post:
I submitted extension to A329164, and A329165. Holding my fingers crossed.
17) Message boards : Number crunching : About Stop@home project (Message 5583)
Posted 12 May 2020 by Tomas Brada
Post:
Dear Natalia. I have a question for you. Is there a use for more tuples of the following type? There are huge amounts of them already.
SPT(14) - 10 million in last batch
TPT(6) - 4 milion in last batch

Yes, the tails are problem of boinc. But it can be improved with configuration. Currently, there is a Pentathlon BOINC running, and many crunchers aborted or abandoned workunits from my project.
18) Message boards : Number crunching : Проект TBEG недоступен (Message 5509)
Posted 26 Apr 2020 by Tomas Brada
Post:
Announce: power outage taken out the server boot filesystem. We restore it from backup. And take time to install battery backup.
19) Message boards : Number crunching : Проект TBEG недоступен (Message 5349)
Posted 2 Mar 2020 by Tomas Brada
Post:
Announce: Forum and server pages are now back online.
20) Message boards : Number crunching : Проект TBEG недоступен (Message 5342)
Posted 1 Mar 2020 by Tomas Brada
Post:
The server received an upgrade of one SSD to replace the presumably faulty HDD. SSD was chosen, because it costs the same as harddrive. I have migrated logical volumes over to the new drive, updated the kernel, updated the operating system, recompiled latest boinc serve and currently I am testing the new drive. I have a small suspicion that there is electrical interference or loose cable somewhere.
Anyway, I re-enabled the file upload handler, so the last outstanding files can be uploaded, even before the database and full operation is resumed.


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