A307170 Minimum number of partial loops in a diagonal Latin square of order n.
0, 0, 0, 12, 0, 21, 0, 24
Offset: 1
Examples
For example, the square 2 4 3 5 0 1 1 0 4 3 2 5 0 2 5 4 1 3 5 3 0 1 4 2 4 5 1 2 3 0 3 1 2 0 5 4 has a loop 2 4 . . . . . . . . . . . 2 . 4 . . . . . . . . 4 . . 2 . . . . . . . . consisting of the sequence of cells L[1,1]=2 -> L[1,2]=4 -> L[3,2]=2 -> L[3,4]=4 -> L[5,4]=2 -> L[5,1]=4 -> L[1,1]=2 with length 6 < 12. The total number of loops for this square is 21, all of which are partial.
Links
- Eduard I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian).
- Eduard I. Vatutin, About the minimum and maximum number of partial loops in a diagonal Latin squares of order 8 (in Russian).
- Eduard I. Vatutin, On the inequalities of the minimum and maximum numerical characteristics of diagonal Latin squares for intercalates, loops and partial loops (in Russian).
- Eduard I. Vatutin, Proving list (best known examples).
- 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.
- Index entries for sequences related to Latin squares and rectangles.
Extensions
a(8) added by Eduard I. Vatutin, Oct 05 2020
Comments