A375475 Number of main classes of diagonalized cyclic diagonal Latin squares of order 2n+1.

1, 0, 1, 1, 7, 81, 2933

Offset: 0

Author

Eduard I. Vatutin, Aug 17 2024

Keywords

• nonn
• more
• hard

Comments

Diagonalized cyclic diagonal Latin squares are diagonal Latin squares that are isomorphic to cyclic Latin squares. They are can be obtained from cyclic Latin squares (see A338522) by diagonalization (getting a corresponding pair of transversals and placing them on the diagonals, see article). Diagonalized cyclic diagonal Latin squares have some interesting properties, for example, there are a large number of diagonal transversals for diagonal Latin squares of odd orders.

Links

• Eduard I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
• Eduard I. Vatutin, About the different types of cyclic diagonal Latin squares (in Russian).
• E. Vatutin, A. Belyshev, N. Nikitina, M. Manzuk, A. Albertian, I. Kurochkin, A. Kripachev, and A. Pykhtin, Diagonalization and Canonization of Latin Squares, Lecture Notes in Computer Science, Vol. 14389, Springer, Cham., 2023. pp. 48-61.
• Proving lists.
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A338522, A338562, A372922, A372923.