A379665 Minimum number of intercalates in a Brown's diagonal Latin square of order 2n.

0, 0, 12, 9, 16, 25

Offset: 0

Author

Eduard I. Vatutin, Dec 29 2024

Keywords

• nonn
• more
• hard

Comments

A Brown's diagonal Latin square is a horizontally symmetric row-inverse or vertically symmetric column-inverse diagonal Latin square (see A339641).

Plain symmetry diagonal Latin squares do not exist for odd orders.

a(6)<=36, a(7)<=49, a(8)<=64, a(9)<=81, a(10)<=100, a(11)<=121, a(12)<=144, a(13)<=201, a(14)<=252. - Updated by Eduard I. Vatutin, Mar 01 2025

Hypothesis: minimum number of intercalates in Brown's diagonal Latin squares of order N=2n is equal to (N/2)^2 for N>4 (proved for N=6 and N=8 using Brute Force and for 10<=N<=24 using heuristic methods).

Links

• Eduard I. Vatutin, On the number of intercalates in diagonal Latin squares of special type, Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2024. pp. 284-286. (in Russian)
• Eduard I. Vatutin, About the minimum number of intercalates in Brown's diagonal Latin squares of orders N<25 (in Russian).
• Eduard I. Vatutin, Proving list (best known examples)
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A307163, A339641.

Extensions

a(5)=25 added by Oleg S. Zaikin and Eduard I. Vatutin, Apr 08 2025