Minimum number of normalized diagonal Latin squares that can be orthogonal to the same diagonal Latin square of order n, https://oeis.org/Axxxxxx

n=1, a(1)=1
Announcement: - (well known fact)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0

n=2, a(2)=0
Announcement: - (well known fact)
-

n=3, a(3)=0
Announcement: - (well known fact)
-

n=4, a(4)=1
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 2 3 1 
3 1 0 2 
1 3 2 0 
2 0 1 3 

n=5, a(5)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 2 3 4 1 
2 1 4 0 3 
4 3 2 1 0 
1 4 0 3 2 
3 0 1 2 4 

n=6, a(6)=0
Announcement: - (well known fact)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 3 4 2 5 1 
2 1 3 5 0 4 
1 5 2 4 3 0 
4 0 5 3 1 2 
5 2 0 1 4 3 
3 4 1 0 2 5 

n=7, a(7)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 3 5 4 2 6 1 
2 1 3 5 6 0 4 
1 4 2 6 5 3 0 
5 6 1 3 0 4 2 
3 0 6 2 4 1 5 
6 2 4 0 1 5 3 
4 5 0 1 3 2 6 

n=8, a(8)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 2 3 7 5 6 4 1 
2 1 5 4 6 7 0 3 
5 4 2 6 7 3 1 0 
1 5 6 3 2 0 7 4 
3 0 7 5 4 1 2 6 
7 6 4 0 1 5 3 2 
4 7 0 1 3 2 6 5 
6 3 1 2 0 4 5 7 

n=9, a(9)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: brute force for source diagonal Latin squares + Euler-Parker method + DLX
0 1 2 3 4 5 6 7 8 
2 3 1 7 8 6 0 5 4 
3 7 8 5 2 1 4 6 0 
8 2 0 4 5 3 7 1 6 
4 5 3 1 6 8 2 0 7 
6 8 4 2 0 7 5 3 1 
5 6 7 8 3 0 1 4 2 
7 0 5 6 1 4 8 2 3 
1 4 6 0 7 2 3 8 5 

n=10, a(10)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: random search for source diagonal Latin squares + Euler-Parker method + DLX
0 1 2 3 4 5 6 7 8 9 
1 2 0 4 5 3 9 8 6 7 
3 5 6 1 8 7 4 0 9 2 
9 4 7 8 3 2 1 6 0 5 
2 7 3 0 9 8 5 1 4 6 
6 8 5 9 2 4 7 3 1 0 
4 6 9 7 0 1 3 2 5 8 
7 0 4 6 1 9 8 5 2 3 
8 3 1 5 6 0 2 9 7 4 
5 9 8 2 7 6 0 4 3 1 

n=11, a(11)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: random search for source diagonal Latin squares + Euler-Parker method + DLX
0 1 2 3 4 5 6 7 8 9 10 
1 2 0 4 5 10 8 9 3 7 6 
5 8 3 7 2 4 9 10 0 6 1 
4 10 7 1 6 8 2 3 9 0 5 
10 0 5 8 7 6 1 4 2 3 9 
6 7 8 10 0 9 4 2 1 5 3 
9 6 10 0 8 3 5 1 7 4 2 
7 4 9 6 10 1 3 8 5 2 0 
8 3 4 2 9 0 10 5 6 1 7 
3 5 6 9 1 2 7 0 4 10 8 
2 9 1 5 3 7 0 6 10 8 4 

n=12, a(12)=0
Announcement: Eduard I. Vatutin, Jun 26 2021 (with corresponding spectrum)
Article: -
Way of finding: random search for source diagonal Latin squares + Euler-Parker method + DLX
0 1 2 3 4 5 6 7 8 9 10 11 
1 2 0 4 5 3 8 6 7 11 9 10 
2 3 4 5 0 1 10 11 6 7 8 9 
10 7 11 6 8 9 2 3 5 0 4 1 
9 11 10 8 7 6 5 4 3 1 0 2 
6 10 7 9 11 8 3 5 4 2 1 0 
11 8 9 7 6 10 1 0 2 4 3 5 
4 5 3 1 2 0 11 9 10 8 6 7 
3 4 5 0 1 2 9 10 11 6 7 8 
5 0 1 2 3 4 7 8 9 10 11 6 
7 6 8 10 9 11 0 2 1 3 5 4 
8 9 6 11 10 7 4 1 0 5 2 3 

Dec 16 2024