A382952 Maximum number of intercalates in an extended self-orthogonal diagonal Latin square of order n.

0, 0, 0, 12, 0, 0, 18, 112, 72, 53

Offset: 1

Author

Eduard I. Vatutin, Apr 09 2025

Keywords

• nonn
• more
• hard

Comments

A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.

Table showing minimums and maximums:

order | 4 5 6 7 8 9 10

min number of intercalates | 12 0 - 0 16 0 5

max number of intercalates | 12 0 - 18 112 72 53 (this sequence)

Links

• Eduard I. Vatutin, About the properties of ESODLS of orders 1-10 (in Russian).
• Eduard I. Vatutin, Proving list, minimum number of intercalates (best known examples).
• Eduard I. Vatutin, Proving list, maximum number of intercalates (best known examples).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A092237, A307164, A309210, A309598, A309599, A360223, A382957.