1,4

A Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 <= m <= n, 1 <= k <= n.

A nontrivial Latin subrectangle is an m X k Latin rectangle of a Latin square of order n, 1 < m < n, 1 < k < n.

E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian).

E. I. Vatutin, About the minimum and maximum number of nontrivial Latin subrectangles in a diagonal Latin squares of order 8 (in Russian).

Eduard Vatutin, Alexey Belyshev, Natalia Nikitina, and Maxim Manzuk, Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10, High-Performance Computing Systems and Technologies in Sci. Res., Automation of Control and Production (HPCST 2020), Communications in Comp. and Inf. Sci. book series (CCIS, Vol. 1304) Springer (2020), 127-146.

Eduard I. Vatutin, Proving list (best known examples).

Index entries for sequences related to Latin squares and rectangles.

For example, the square

0 1 2 3 4 5 6

4 2 6 5 0 1 3

3 6 1 0 5 2 4

6 3 5 4 1 0 2

1 5 3 2 6 4 0

5 0 4 6 2 3 1

2 4 0 1 3 6 5

has a nontrivial Latin subrectangle

. . . . . . .

. . 6 5 0 1 3

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . 0 1 3 6 5

The total number of Latin subrectangles for this square is 2119 and the number of nontrivial Latin subrectangles is only 151.

Cf. A307839, A307842.

Sequence in context: A333577 A278711 A331911 * A257949 A375664 A375680

Adjacent sequences: A307838 A307839 A307840 * A307842 A307843 A307844

nonn,more,hard

Eduard I. Vatutin, May 01 2019

a(8) added by Eduard I. Vatutin, Oct 06 2020

approved