Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n, https://oeis.org/Axxxxxx n=1, a(1)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: trivial 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=12 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX 0 1 2 3 2 3 0 1 3 2 1 0 1 0 3 2 n=5, a(5)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX 0 1 2 3 4 2 3 4 0 1 4 0 1 2 3 1 2 3 4 0 3 4 0 1 2 n=6, a(6)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX (for n=6 ODLS does not exist) - n=7, a(7)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX 0 1 2 3 4 5 6 2 3 1 5 6 4 0 5 6 4 0 1 2 3 4 0 6 2 3 1 5 6 2 0 1 5 3 4 1 5 3 4 0 6 2 3 4 5 6 2 0 1 n=8, a(8)=2 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX 0 1 2 3 4 5 6 7 1 2 0 5 7 6 4 3 4 6 5 7 1 3 0 2 6 7 3 4 0 1 2 5 3 0 7 1 6 2 5 4 5 4 6 2 3 7 1 0 7 5 1 0 2 4 3 6 2 3 4 6 5 0 7 1 n=9, a(9)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: brute force, Euler-Parker method, DLX 0 1 2 3 4 5 6 7 8 2 3 4 8 0 6 7 5 1 8 6 1 7 3 0 2 4 5 7 0 5 2 6 3 8 1 4 5 2 6 4 7 8 1 3 0 3 5 8 6 1 4 0 2 7 4 8 0 1 2 7 5 6 3 6 4 7 0 5 1 3 8 2 1 7 3 5 8 2 4 0 6 n=10, a(10)<=2 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: different generators of DLS, Euler-Parker method, DLX 0 1 2 3 4 5 6 7 8 9 1 2 0 4 5 7 3 9 6 8 4 6 5 7 9 8 0 2 1 3 3 7 1 8 2 0 4 6 9 5 9 3 6 0 7 1 5 8 4 2 5 9 7 6 8 4 1 3 2 0 2 8 4 5 6 3 9 0 7 1 8 4 3 9 0 6 2 1 5 7 6 0 8 2 1 9 7 5 3 4 7 5 9 1 3 2 8 4 0 6 n=11, a(11)=0 Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021 Way of finding: random search of DLS, Euler-Parker method, DLX 0 1 2 3 4 5 6 7 8 9 10 2 3 1 4 5 6 7 9 10 8 0 6 9 7 8 10 0 2 1 4 3 5 7 8 9 10 0 2 1 3 5 4 6 1 4 3 5 6 7 9 8 0 10 2 9 10 8 0 2 1 3 4 6 5 7 3 5 4 6 7 9 8 10 2 0 1 8 0 10 2 1 3 4 5 7 6 9 10 2 0 1 3 4 5 6 9 7 8 4 6 5 7 9 8 10 0 1 2 3 5 7 6 9 8 10 0 2 3 1 4 n=12, a(12)<=4 Announcement: -, Eduard I. Vatutin, before Jul 21 2022 Way of finding: random search of DLS, Euler-Parker method, DLX 0 1 2 3 4 5 6 7 8 9 10 11 1 2 0 4 5 7 9 10 6 11 3 8 3 9 6 5 1 11 10 4 2 8 0 7 10 8 3 11 2 9 0 5 4 7 6 1 4 3 5 8 9 0 1 6 11 2 7 10 5 7 10 6 8 3 2 11 1 0 4 9 8 0 4 2 7 1 5 9 10 6 11 3 6 11 1 7 10 2 4 8 9 3 5 0 2 10 11 0 3 4 8 1 7 5 9 6 11 4 9 1 0 6 7 2 3 10 8 5 9 5 7 10 6 8 11 3 0 4 1 2 7 6 8 9 11 10 3 0 5 1 2 4 n=13, a(13)=0 Announcement: -, Eduard I. Vatutin, Jul 21 2022 Way of finding: cyclic square 0 1 2 3 4 5 6 7 8 9 10 11 12 3 4 5 6 7 8 9 10 11 12 0 1 2 6 7 8 9 10 11 12 0 1 2 3 4 5 9 10 11 12 0 1 2 3 4 5 6 7 8 12 0 1 2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11 12 0 1 5 6 7 8 9 10 11 12 0 1 2 3 4 8 9 10 11 12 0 1 2 3 4 5 6 7 11 12 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 0 4 5 6 7 8 9 10 11 12 0 1 2 3 7 8 9 10 11 12 0 1 2 3 4 5 6 10 11 12 0 1 2 3 4 5 6 7 8 9 Jul 21 2022