Minimum number of ODLS in Brown's diagonal Latin squares of order N=2n, https://oeis.org/Axxxxxx

n=2, a(2)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
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n=4, a(4)=1
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 
2 3 0 1 
3 2 1 0 
1 0 3 2 

n=6, a(6)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 
1 2 0 5 3 4 
4 3 5 0 2 1 
3 0 1 4 5 2 
5 4 3 2 1 0 
2 5 4 1 0 3 

n=8, a(8)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 6 7 
1 2 3 0 5 7 4 6 
5 4 6 7 0 1 3 2 
4 6 7 5 3 2 0 1 
7 5 4 6 1 0 2 3 
6 7 5 4 2 3 1 0 
3 0 1 2 6 4 7 5 
2 3 0 1 7 6 5 4 

n=10, a(10)=0
Announcement: -, Eduard I. Vatutin, Dec 22 2024
Way of finding: random search
0 1 2 3 4 5 6 7 8 9 
1 2 0 4 6 3 5 9 7 8 
2 3 4 9 1 8 0 5 6 7 
8 7 9 5 3 6 4 0 2 1 
7 6 5 0 8 1 9 4 3 2 
5 9 3 1 2 7 8 6 0 4 
9 8 7 6 5 4 3 2 1 0 
6 4 8 2 9 0 7 1 5 3 
4 0 6 8 7 2 1 3 9 5 
3 5 1 7 0 9 2 8 4 6 

n=12, a(12)=0
Announcement: -, Eduard I. Vatutin, Dec 22 2024
Way of finding: for diagonal transversals spectrum
0 1 2 3 4 5 6 7 8 9 10 11 
11 10 9 8 7 6 5 4 3 2 1 0 
1 9 4 0 5 3 8 6 11 7 2 10 
4 8 0 6 2 1 10 9 5 11 3 7 
7 3 11 5 9 10 1 2 6 0 8 4 
10 2 7 11 6 8 3 5 0 4 9 1 
2 6 3 10 0 4 7 11 1 8 5 9 
8 11 5 7 10 9 2 1 4 6 0 3 
5 4 10 9 8 11 0 3 2 1 7 6 
9 5 8 1 11 7 4 0 10 3 6 2 
3 0 6 4 1 2 9 10 7 5 11 8 
6 7 1 2 3 0 11 8 9 10 4 5 

n=14, a(14)=0
Announcement: -, Eduard I. Vatutin, Dec 22 2024
Way of finding: for diagonal transversals spectrum
0 1 2 3 4 5 6 7 8 9 10 11 12 13 
1 2 3 0 5 6 7 13 10 11 9 8 4 12 
11 4 10 7 2 8 3 0 6 12 13 5 1 9 
4 8 7 9 3 10 0 1 13 5 12 6 2 11 
8 13 9 5 12 0 11 6 1 3 4 7 10 2 
12 11 6 10 8 3 13 9 7 4 0 2 5 1 
13 12 5 6 11 4 8 10 2 0 3 1 9 7 
5 6 13 12 10 7 9 11 0 2 1 3 8 4 
6 10 12 11 9 1 5 8 4 7 2 0 13 3 
9 5 8 13 6 2 10 12 3 1 7 4 11 0 
7 9 4 8 1 11 2 3 5 13 6 12 0 10 
10 7 11 4 0 9 1 2 12 6 5 13 3 8 
3 0 1 2 13 12 4 5 11 10 8 9 7 6 
2 3 0 1 7 13 12 4 9 8 11 10 6 5 

Dec 22 2024