Minimum number of diagonal transversals in a diagonal Latin square of order n, https://oeis.org/A287647 n=1, a(1)=1 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=4 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 3 2 1 0 1 0 3 2 2 3 0 1 n=5, a(5)=1 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 4 2 0 1 3 1 4 3 2 0 3 0 1 4 2 2 3 4 0 1 n=6, a(6)=2 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 4 2 5 0 3 1 3 5 1 2 0 4 5 3 0 4 1 2 2 4 3 1 5 0 1 0 4 5 2 3 n=7, a(7)=0 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 6 6 2 4 5 1 0 3 5 0 1 6 2 3 4 3 5 6 4 0 1 2 2 6 5 1 3 4 0 4 3 0 2 5 6 1 1 4 3 0 6 2 5 n=8, a(8)=0 Article: E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, S. Yu. Valyaev, Enumerating the Transversals for Diagonal Latin Squares of Small Order. CEUR Workshop Proceedings. Proceedings of the Third International Conference BOINC-based High Performance Computing: Fundamental Research and Development (BOINC:FAST 2017). Vol. 1973. Technical University of Aachen, Germany, 2017. pp. 6-14. urn:nbn:de:0074-1973-0. http://ceur-ws.org/Vol-1973/paper01.pdf Way of finding: brute force 0 1 2 3 4 5 6 7 1 2 0 4 3 7 5 6 7 0 1 6 5 4 2 3 4 6 7 5 1 0 3 2 3 7 5 0 6 2 4 1 5 4 6 7 2 3 1 0 6 3 4 2 0 1 7 5 2 5 3 1 7 6 0 4 n=9, a(9)=0 Announcement: https://vk.com/wall162891802_1335, Eduard I. Vatutin, Natalia N. Nikitina, Maxim O. Manzuk, Sep 10 2020 Way of finding: brute force using X-based fillings 0 2 3 4 5 7 8 6 1 5 1 6 7 3 8 4 0 2 6 0 2 8 7 1 3 5 4 1 5 7 3 8 2 0 4 6 2 6 1 5 4 0 7 8 3 4 7 8 6 2 5 1 3 0 8 3 5 1 0 4 6 2 7 3 8 4 0 1 6 2 7 5 7 4 0 2 6 3 5 1 8 n=10, a(10)<=15 Announcement: https://vk.com/wall162891802_1546, Eduard I. Vatutin, Feb 25 2021 Way of finding: random search in the neighborhood of central symmetry 0 1 2 3 4 5 6 7 8 9 1 2 0 4 3 7 9 8 6 5 2 4 9 6 8 1 3 5 0 7 3 5 7 1 9 8 0 2 4 6 9 6 4 5 7 3 8 1 2 0 8 3 5 0 2 6 1 9 7 4 7 9 3 8 0 4 5 6 1 2 6 8 1 2 5 0 7 4 9 3 5 7 8 9 6 2 4 0 3 1 4 0 6 7 1 9 2 3 5 8 n=11, a(11)<=279 Announcement: https://vk.com/wall162891802_1565, Eduard I. Vatutin, Mar 06 2021 Way of finding: random search in the neighborhood of central symmetry 0 1 2 3 4 5 6 7 8 9 10 1 2 3 10 5 9 8 4 6 7 0 3 4 10 7 1 6 0 5 9 8 2 5 3 9 1 8 10 7 0 2 6 4 9 0 8 6 7 4 3 2 10 5 1 4 10 0 5 2 8 1 6 7 3 9 8 7 5 2 6 0 9 10 4 1 3 7 8 6 4 9 2 10 3 1 0 5 10 6 1 9 0 3 4 8 5 2 7 6 5 7 0 10 1 2 9 3 4 8 2 9 4 8 3 7 5 1 0 10 6 n=12, a(12)<=1200 Announcement: https://vk.com/wall162891802_1603, Eduard I. Vatutin, Mar 25 2021 Way of finding: random search in the neighborhood of central symmetry + neighborhood based improvement 0 10 6 4 9 3 2 8 5 7 11 1 11 1 5 7 2 8 9 3 6 4 0 10 7 5 2 8 10 0 1 11 9 3 4 6 4 6 9 3 1 11 10 0 2 8 7 5 8 2 11 1 4 6 7 5 0 10 3 9 3 9 0 10 7 5 4 6 11 1 8 2 9 3 10 0 5 7 6 4 1 11 2 8 2 8 1 11 6 4 5 7 10 0 9 3 6 4 3 9 11 1 0 10 8 2 5 7 5 7 8 2 0 10 11 1 3 9 6 4 1 11 7 5 8 2 3 9 4 6 10 0 10 0 4 6 3 9 8 2 7 5 1 11 n=13, a(13)<=9700 Announcement: https://vk.com/wall162891802_1605, Eduard I. Vatutin, Mar 25 2021 Way of finding: random search + neighborhood based improvement 7 1 0 3 6 5 12 2 8 9 10 11 4 2 3 4 10 0 7 6 9 12 11 5 8 1 4 11 1 7 8 9 10 3 6 0 12 2 5 6 5 8 11 10 4 7 0 1 2 3 9 12 8 9 2 5 12 11 1 4 3 10 0 6 7 3 6 12 0 1 2 8 11 5 4 7 10 9 10 0 3 2 9 12 5 6 7 8 1 4 11 1 7 10 4 3 6 9 8 2 5 11 12 0 11 4 5 6 7 0 3 10 9 12 2 1 8 5 8 7 1 4 10 11 12 0 6 9 3 2 12 2 9 8 11 1 0 7 10 3 4 5 6 9 10 11 12 5 8 2 1 4 7 6 0 3 0 12 6 9 2 3 4 5 11 1 8 7 10 Mar 25 2021