A360221 Minimum number of intercalates in an orthogonal diagonal Latin square of order n.

0, 0, 0, 12, 0, 0, 0, 2, 0

Offset: 1

Author

Eduard I. Vatutin, Jan 30 2023

Keywords

• nonn
• more
• hard
• bref

Comments

An intercalate is a 2 X 2 subsquare of a Latin square.

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

a(10) <= 1, a(11) = 0, a(12) <= 4, a(13) = 0. - Eduard I. Vatutin, added Jan 30 2023, updated Sep 24 2024

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. A305570, A305571, A307163, A354050, A360223.