A382957 -id:A382957 - cp's OEIS frontend

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

Eduard I. Vatutin, Apr 09 2025

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)

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.

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

cp's OEIS Frontend

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

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