Minimum number of diagonal transversals 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)=4
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)=2
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 7 4 5 6 
4 5 6 7 0 3 2 1 
5 6 7 4 1 0 3 2 
7 4 5 6 3 2 1 0 
6 7 4 5 2 1 0 3 
3 0 1 2 5 6 7 4 
2 3 0 1 6 7 4 5 

n=10, a(10)<=24
Announcement: -, Eduard I. Vatutin, Dec 16 2024
Way of finding: random search, from experiments with spectra
0 1 2 3 4 5 6 7 8 9 
1 2 0 4 5 3 7 9 6 8 
6 7 1 5 9 8 4 2 3 0 
2 9 7 8 3 6 1 0 4 5 
8 4 9 6 7 0 2 5 1 3 
7 0 6 9 8 4 3 1 5 2 
3 6 8 7 2 9 5 4 0 1 
9 8 5 1 6 7 0 3 2 4 
5 3 4 0 1 2 8 6 9 7 
4 5 3 2 0 1 9 8 7 6 

n=12, a(12)<=1120
Announcement: -, Eduard I. Vatutin, Dec 16 2024
Way of finding: random search, from experiments with spectra
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)<=7604
Announcement: -, Eduard I. Vatutin, Feb 18 2022
Way of finding: random search, from experiments with spectra
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 

n=16, a(16)<=1120090
Announcement: -, Eduard I. Vatutin, Jan 23 2022
Way of finding: random search, from experiments with spectra
0 1 2 3 4 10 6 7 8 9 15 11 12 13 14 5 
11 15 1 2 9 7 12 0 5 3 8 6 13 14 10 4 
12 4 8 15 5 14 13 6 9 2 1 0 10 7 11 3 
8 5 12 9 13 11 1 15 10 14 4 2 6 3 0 7 
5 14 13 12 11 15 9 8 7 6 10 4 3 2 1 0 
15 13 0 7 14 6 4 3 12 11 9 1 8 5 2 10 
14 6 4 5 15 12 7 13 2 8 3 10 0 11 9 1 
10 2 5 8 1 9 11 12 3 4 6 14 7 0 13 15 
6 8 15 4 3 13 0 14 1 5 2 12 11 10 7 9 
13 3 9 1 8 0 15 11 4 10 5 7 14 6 12 2 
3 11 7 10 0 1 2 9 6 13 14 5 15 8 4 12 
9 7 10 11 12 2 5 1 14 0 13 3 4 15 8 6 
4 10 14 13 6 8 3 5 0 12 7 9 2 1 15 11 
1 9 11 0 10 3 8 2 13 7 12 15 5 4 6 14 
7 0 3 6 2 4 14 10 15 1 11 13 9 12 5 8 
2 12 6 14 7 5 10 4 11 15 0 8 1 9 3 13 

Dec 22 2024