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Diagonal Latin squares of order n>10

Diagonal Latin squares of order n>10

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Natalia Makarova
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Message 4241 - Posted: 17 Aug 2020, 18:33:10 UTC - in response to Message 4240.  
Last modified: 17 Aug 2020, 18:33:28 UTC

I could try enumerating orthogonal mates of F98aux31EFfDjHASPckbbhZCsweDB7qd3dcgExK6yTQ75FDD3, would that help? I need to modify my program. To enumerate all, it would take long time. Maybe for a boinc project?

This will help, but will not completely solve the problem.
There is a more interesting and solvable problem for BOINC - DB CF ODLS of order 9
https://boinc.tbrada.eu/forum_thread.php?id=3114
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Message 4242 - Posted: 18 Aug 2020, 1:31:00 UTC - in response to Message 4240.  

What did found is that there is 23040*8 isomorphisms of order 12 and 13, and 322560*8 isomorphisms of order 14.

See
https://oeis.org/A299784
It seems that a(n) = 2^m * m! * 4 for all n > 6.
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Message 4243 - Posted: 18 Aug 2020, 15:28:58 UTC

Related:
https://oeis.org/A000316
https://oeis.org/A309283
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Message 4244 - Posted: 18 Aug 2020, 15:41:24 UTC
Last modified: 18 Aug 2020, 16:12:20 UTC

Order 7:
x-fillings: 80
rules: 3
isotopes: 24*8 (192)
Order 8:
x-fillings: 4752
rules: 20
isotopes: 192*8 (1536)
Order 9:
x-fillings: 4752
rules: 20
isotopes: 192*8 (1536)
Order 10:
x-fillings: 440192
rules: 67
isotopes: 1920 *8 (15360)
Order 11:
x-fillings: 440192
rules: 67
isotopes: 1920 *8 (15360)
Order 12:
x-fillings: 59245120?
rules: 596?
isotopes: 23040*8 (184320)

The sequence 80, 4752, 440192 is A000316:
Count of x-fillings of DLS(n*2).
Two decks each have n kinds of cards, 2 of each kind. The first deck is laid out in order. The second deck is shuffled and laid out next to the first. A match occurs if a card from the second deck is next to a card of the same kind from the first deck. a(n) is the number of ways of achieving no matches.
Which is exactly what x-filling is. Again connecting Latin squares and card games.
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Message 4260 - Posted: 19 Aug 2020, 0:46:40 UTC - in response to Message 4244.  
Last modified: 19 Aug 2020, 0:47:05 UTC

Tomáš Brada
I posted the rules for SN DLS of order 12, 13 and 14
https://yadi.sk/d/6tkvilMwqzHDlA

Please check.
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Message 4265 - Posted: 20 Aug 2020, 16:39:28 UTC - in response to Message 4239.  

How many rules did you find for SN DLS of order 14?
I have found 278 rules so far. I have very few CF ODLS of this order.

I have found 911 rules so far.
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Message 4266 - Posted: 20 Aug 2020, 17:20:17 UTC - in response to Message 4265.  

How many rules did you find for SN DLS of order 14?
I have found 278 rules so far. I have very few CF ODLS of this order.

I have found 911 rules so far.

Please publish the corresponding 911 CFs.
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Message 4276 - Posted: 7 Sep 2020, 3:38:38 UTC

I have found 1264 rules for SN ODLS of order 14 so far.
See
https://boinc.progger.info/odlk/forum_thread.php?id=162&postid=6340#6340
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Message 4277 - Posted: 7 Sep 2020, 8:32:19 UTC - in response to Message 4276.  

I have found 3483 rules for SN ODLS of order 14. The program was taking too long, I stopped it.
https://hr.tbrada.eu/tomas/rules14.txt
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Message 4278 - Posted: 7 Sep 2020, 13:04:32 UTC - in response to Message 4277.  
Last modified: 7 Sep 2020, 13:05:44 UTC

I have found 3483 rules for SN ODLS of order 14. The program was taking too long, I stopped it.
https://hr.tbrada.eu/tomas/rules14.txt

I need GFs ODLS (format 2) for verification.
Can you post?

I compared the first 20 rules, they do not match.
This is normal.

your
1 0 3 2 5 4 8 9 6 7 11 10 13 12
1 0 3 2 5 4 8 9 6 7 11 12 13 10
1 0 3 2 5 4 8 9 6 7 12 13 10 11
1 0 3 2 5 4 8 9 6 7 12 13 11 10
1 0 3 2 5 4 8 9 6 10 7 12 13 11
1 0 3 2 5 4 8 9 6 10 11 7 13 12
1 0 3 2 5 4 8 9 6 10 11 12 13 7
1 0 3 2 5 4 8 9 6 10 12 7 13 11
1 0 3 2 5 4 8 9 6 10 12 13 7 11
1 0 3 2 5 4 8 9 6 10 12 13 11 7
1 0 3 2 5 4 8 9 7 6 11 10 13 12
1 0 3 2 5 4 8 9 7 6 11 12 13 10
1 0 3 2 5 4 8 9 7 6 12 13 10 11
1 0 3 2 5 4 8 9 7 6 12 13 11 10
1 0 3 2 5 4 8 9 7 10 6 12 13 11
1 0 3 2 5 4 8 9 7 10 11 6 13 12
1 0 3 2 5 4 8 9 7 10 11 12 13 6
1 0 3 2 5 4 8 9 7 10 12 6 13 11
1 0 3 2 5 4 8 9 7 10 12 13 6 11
1 0 3 2 5 4 8 9 7 10 12 13 11 6
. . . . . . 

my
 1  0  3  2  5  4  8  9  6  7 11 10 13 12
 1  0  3  2  5  4  8  9  6  7 12 13 10 11
 1  0  3  2  5  4  8  9  7 10  6 12 13 11
 1  0  3  2  5  4  8  9  7 10 12 13 11  6
 1  0  3  2  5  4  8  9 10 11  6 12 13  7
 1  0  3  2  5  4  8  9 10 11  7  6 13 12
 1  0  3  2  5  4  8  9 10 12  6 13 11  7
 1  0  3  2  5  4  8  9 10 12  7 13 11  6
 1  0  3  2  5  4  8 10  6 11  7  9 13 12
 1  0  3  2  5  4  8 10  6 12  7 13  9 11
 1  0  3  2  5  4  8 10  6 12 11  9 13  7
 1  0  3  2  5  4  8 10  7 11  6 12 13  9
 1  0  3  2  5  4  8 10  7 11 12  6 13  9
 1  0  3  2  5  4  8 10  7 11 12  9 13  6
 1  0  3  2  5  4  8 10  7 12  9 13 11  6
 1  0  3  2  5  4  8 10  9  6 12 13  7 11
 1  0  3  2  5  4  8 10  9 12 13  6 11  7
 1  0  3  2  5  4  8 10  9 12 13  7  6 11
 1  0  3  2  5  4  8 10  9 12 13  7 11  6
 1  0  3  2  5  4  8 10 11  6 12 13  7  9
. . . . . . 
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Message 4280 - Posted: 8 Sep 2020, 6:15:15 UTC

Harry White found 5225 rules for order 14 as well as for order 15.
See
https://boinc.progger.info/odlk/forum_thread.php?id=162&postid=6345
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Message 4338 - Posted: 28 Nov 2020, 16:11:29 UTC
Last modified: 28 Nov 2020, 16:24:48 UTC

Tomáš Brada
Please confirm the number of D-transversals for this DLK
H8YURdMXZnihqsPkArWe9CwrZqH62bHYQ3MY81AmSxkqDU4UM8WFe3ncZMbpZr5


I counted 31313088 D-transversals with your program ortogonb.exe.
Is it correct?

See
https://boinc.progger.info/odlk/forum_thread.php?id=162&postid=6926
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Message 4339 - Posted: 30 Nov 2020, 10:13:30 UTC - in response to Message 4338.  

I will get to it tomorrow.
Hurray!
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Message 4340 - Posted: 1 Dec 2020, 14:29:37 UTC - in response to Message 4339.  

I will get to it tomorrow.
Hurray!

Hurray!
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Message 4342 - Posted: 2 Dec 2020, 2:45:11 UTC - in response to Message 4339.  
Last modified: 2 Dec 2020, 2:45:47 UTC

I will get to it tomorrow.
Hurray!

Have you got tomorrow yet? :)
Are you joking?

Hurray! :)
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Message 4344 - Posted: 1 Jan 2021, 11:48:41 UTC

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Message 4349 - Posted: 6 Jan 2021, 6:53:40 UTC
Last modified: 6 Jan 2021, 16:45:05 UTC

A task

This DLS of order 12 has 24901 d-transversals (the maximum currently known).



See https://oeis.org/A287648

It is required to find all orthogonal DLSs for this DLS.
Program here
https://boinc.tbrada.eu/forum_thread.php?id=3104&postid=4166

Here's another program (by Belyshev)
https://yadi.sk/d/rW8gHaJgwLh3DA

This program runs in one thread.
Run the ortogon_u.exe program by double-clicking the left mouse button.
On the program request, enter the DLS order, it is 12.

PS. Code of square
DW71H14GBTJeK6fE1RcSBVdKdAhrHJYM

The code is needed for the first program (by Tomáš Brada).
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Message 4350 - Posted: 9 Jan 2021, 10:16:38 UTC - in response to Message 4349.  
Last modified: 9 Jan 2021, 10:17:17 UTC

You can interrupt the Belyshev's program (Ctrl + C) with some result.
Solutions will be written to the mates.txt file.
It takes a long time to complete the program.
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Message 4352 - Posted: 10 Jan 2021, 18:35:36 UTC

In my article “Mutually Orthogonal Latin Squares (MOLS)”
http://www.natalimak1.narod.ru/grolk2.htm
showing four squares from MOLS of order 27.

These are two DLS

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
3 4 5 6 7 8 0 1 2 12 13 14 15 16 17 9 10 11 21 22 23 24 25 26 18 19 20
6 7 8 0 1 2 3 4 5 15 16 17 9 10 11 12 13 14 24 25 26 18 19 20 21 22 23
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0 1 2 3 4 5 6 7 8
12 13 14 15 16 17 9 10 11 21 22 23 24 25 26 18 19 20 3 4 5 6 7 8 0 1 2
15 16 17 9 10 11 12 13 14 24 25 26 18 19 20 21 22 23 6 7 8 0 1 2 3 4 5
18 19 20 21 22 23 24 25 26 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
21 22 23 24 25 26 18 19 20 3 4 5 6 7 8 0 1 2 12 13 14 15 16 17 9 10 11
24 25 26 18 19 20 21 22 23 6 7 8 0 1 2 3 4 5 15 16 17 9 10 11 12 13 14
13 14 12 16 17 15 10 11 9 22 23 21 25 26 24 19 20 18 4 5 3 7 8 6 1 2 0
16 17 15 10 11 9 13 14 12 25 26 24 19 20 18 22 23 21 7 8 6 1 2 0 4 5 3
10 11 9 13 14 12 16 17 15 19 20 18 22 23 21 25 26 24 1 2 0 4 5 3 7 8 6
22 23 21 25 26 24 19 20 18 4 5 3 7 8 6 1 2 0 13 14 12 16 17 15 10 11 9
25 26 24 19 20 18 22 23 21 7 8 6 1 2 0 4 5 3 16 17 15 10 11 9 13 14 12
19 20 18 22 23 21 25 26 24 1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16 17 15
4 5 3 7 8 6 1 2 0 13 14 12 16 17 15 10 11 9 22 23 21 25 26 24 19 20 18
7 8 6 1 2 0 4 5 3 16 17 15 10 11 9 13 14 12 25 26 24 19 20 18 22 23 21
1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16 17 15 19 20 18 22 23 21 25 26 24
26 24 25 20 18 19 23 21 22 8 6 7 2 0 1 5 3 4 17 15 16 11 9 10 14 12 13
20 18 19 23 21 22 26 24 25 2 0 1 5 3 4 8 6 7 11 9 10 14 12 13 17 15 16
23 21 22 26 24 25 20 18 19 5 3 4 8 6 7 2 0 1 14 12 13 17 15 16 11 9 10
8 6 7 2 0 1 5 3 4 17 15 16 11 9 10 14 12 13 26 24 25 20 18 19 23 21 22
2 0 1 5 3 4 8 6 7 11 9 10 14 12 13 17 15 16 20 18 19 23 21 22 26 24 25
5 3 4 8 6 7 2 0 1 14 12 13 17 15 16 11 9 10 23 21 22 26 24 25 20 18 19
17 15 16 11 9 10 14 12 13 26 24 25 20 18 19 23 21 22 8 6 7 2 0 1 5 3 4
11 9 10 14 12 13 17 15 16 20 18 19 23 21 22 26 24 25 2 0 1 5 3 4 8 6 7
14 12 13 17 15 16 11 9 10 23 21 22 26 24 25 20 18 19 5 3 4 8 6 7 2 0 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
4 5 3 7 8 6 1 2 0 13 14 12 16 17 15 10 11 9 22 23 21 25 26 24 19 20 18
8 6 7 2 0 1 5 3 4 17 15 16 11 9 10 14 12 13 26 24 25 20 18 19 23 21 22
12 13 14 15 16 17 9 10 11 21 22 23 24 25 26 18 19 20 3 4 5 6 7 8 0 1 2
16 17 15 10 11 9 13 14 12 25 26 24 19 20 18 22 23 21 7 8 6 1 2 0 4 5 3
11 9 10 14 12 13 17 15 16 20 18 19 23 21 22 26 24 25 2 0 1 5 3 4 8 6 7
24 25 26 18 19 20 21 22 23 6 7 8 0 1 2 3 4 5 15 16 17 9 10 11 12 13 14
19 20 18 22 23 21 25 26 24 1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16 17 15
23 21 22 26 24 25 20 18 19 5 3 4 8 6 7 2 0 1 14 12 13 17 15 16 11 9 10
22 23 21 25 26 24 19 20 18 4 5 3 7 8 6 1 2 0 13 14 12 16 17 15 10 11 9
26 24 25 20 18 19 23 21 22 8 6 7 2 0 1 5 3 4 17 15 16 11 9 10 14 12 13
18 19 20 21 22 23 24 25 26 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
7 8 6 1 2 0 4 5 3 16 17 15 10 11 9 13 14 12 25 26 24 19 20 18 22 23 21
2 0 1 5 3 4 8 6 7 11 9 10 14 12 13 17 15 16 20 18 19 23 21 22 26 24 25
3 4 5 6 7 8 0 1 2 12 13 14 15 16 17 9 10 11 21 22 23 24 25 26 18 19 20
10 11 9 13 14 12 16 17 15 19 20 18 22 23 21 25 26 24 1 2 0 4 5 3 7 8 6
14 12 13 17 15 16 11 9 10 23 21 22 26 24 25 20 18 19 5 3 4 8 6 7 2 0 1
15 16 17 9 10 11 12 13 14 24 25 26 18 19 20 21 22 23 6 7 8 0 1 2 3 4 5
17 15 16 11 9 10 14 12 13 26 24 25 20 18 19 23 21 22 8 6 7 2 0 1 5 3 4
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0 1 2 3 4 5 6 7 8
13 14 12 16 17 15 10 11 9 22 23 21 25 26 24 19 20 18 4 5 3 7 8 6 1 2 0
20 18 19 23 21 22 26 24 25 2 0 1 5 3 4 8 6 7 11 9 10 14 12 13 17 15 16
21 22 23 24 25 26 18 19 20 3 4 5 6 7 8 0 1 2 12 13 14 15 16 17 9 10 11
25 26 24 19 20 18 22 23 21 7 8 6 1 2 0 4 5 3 16 17 15 10 11 9 13 14 12
5 3 4 8 6 7 2 0 1 14 12 13 17 15 16 11 9 10 23 21 22 26 24 25 20 18 19
6 7 8 0 1 2 3 4 5 15 16 17 9 10 11 12 13 14 24 25 26 18 19 20 21 22 23
1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16 17 15 19 20 18 22 23 21 25 26 24


Need find the rest of the DLS.
This can be done in the Maple mathematical software package.
The command MOLS(3,3,26) may need to be used.

Can someone do this?
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Message 4353 - Posted: 11 Jan 2021, 15:35:01 UTC
Last modified: 26 Jan 2021, 10:48:35 UTC

Releasing programs for DLK(N).
Source on: https://github.com/tomasbrod/tbboinc
Download windows build ec0d025846:
https://boinc.tbrada.eu/download/ndlk-2101a.zip
Download windows build b1b4dc24f04:
https://boinc.tbrada.eu/download/ndlk-2101b.zip

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)


ortogonb.exe
ortogonb.exe: [-co] (Input) >output
** Search for Orthogonal mates of Diagonal Latin Square **
 -c print number of transverses and exit
 -o output orthogonal mates like they are found
Input: encoded diagonal latin square (see dlkconv.exe)
Output: metadata and orthogonal squares in encoded format
Returns 0 if orthogonal mates found, 1 if not. Multi Thread.
Example ortogonb.exe BJMzz45jMmo1FfZtCjN
Author: Tomas Brada (GPL)


ortogonbw.exe
ortogonbw.exe: (Input) (Path) >output
** Search for Orthogonal mates of Diagonal Latin Square **
Input: encoded diagonal latin square (see dlkconv.exe)
Output: metadata and orthogonal squares in encoded format
Prints to output immediately as square is found. Single thread.
Path: sequence of space-separated numbers narrowing the problem space
Explanation: L(level) c(column) choosen-row / count-rows
Specify number as Path from 1 up to count-rows to narrow down the Search,
specify multiple numbers to narrow down further.
Example: ortogonbw.exe DeGkNZGc43qaHWnNUsjfvuQNbREDKc4 3 120
Author: Tomas Brada (GPL)


kanonb.exe
kanonb.exe: <input >output
** Diagonal Latin Square Kanonizer **
Input and Output in Encoded form (see dlkconv)
Uses cache files kanonb_cache_NN.dat in the current directory.


ortowalk.exe
ortowalk.exe: FileName
** Explore the full graph of DLK orthogonality **
Insert the initial CF-DLK into FileName.todo
then run "ortowalk.exe FileName" (without the .todo)
Author: Tomas Brada (GPL)


rules.exe
rules.exe: (N) >output
** Diagonal Latin Square Rule Enumerator **
Enumerates all rules of CF-DLK of order N
Uses cache files kanonb_cache_NN.dat in the current directory.
Author: Tomas Brada (GPL)
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