A360223 Maximum number of intercalates in an orthogonal diagonal Latin square of order n.

0, 0, 0, 12, 0, 0, 18, 112, 72

Offset

1,4

Comments

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

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

a(10) >= 76, a(11) >= 94, a(12) >= 324, a(13) >= 26. - Eduard I. Vatutin, updated Feb 25 2024

Links

Table of n, a(n) for n=1..9.

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, A307164, A354050, A360221.

Sequence in context: A369349 A368816 A004012 * A270256 A072837 A023917

Adjacent sequences: A360220 A360221 A360222 * A360224 A360225 A360226

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jan 30 2023

Status

approved