A360220 Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n.

1, 0, 0, 4, 5, 0, 27, 120, 333

Offset: 1

Author

Eduard I. Vatutin, Jan 30 2023

Keywords

• nonn
• more
• hard

Comments

An orthogonal diagonal Latin square is a diagonal Latin square that has at least one orthogonal diagonal mate.

a(10) >= 866, a(11) >= 4828, a(12) >= 30192, a(13) >= 131106, a(17) >= 204995269, a(19) >= 11254190082.

For most orders n, at least one diagonal Latin square with the maximal number of diagonal transversals has an orthogonal mate and A287648(n) = a(n). Known exceptions: n=6 and n=10. - Eduard I. Vatutin, Feb 17 2023

Every orthogonal diagonal Latin square is a diagonal Latin square, so A287647(n) <= A354068(n) <= a(n) <= A287648(n). - Eduard I. Vatutin, Mar 04 2023

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).
• Eduard I. Vatutin, Proving list (best known examples).
• E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021), Tula, 2021, pp. 7-17. (in Russian)
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A287647, A287648, A305570, A305571, A349199, A354068.