A307841 Minimum number of nontrivial Latin subrectangles in a diagonal Latin square of order n.
0, 0, 0, 12, 0, 51, 0, 36
Offset: 1
Examples
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.
Links
- 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.
Extensions
a(8) added by Eduard I. Vatutin, Oct 06 2020
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