A307163
Minimum number of intercalates in a diagonal Latin square of order n.
Original entry on oeis.org
0, 0, 0, 12, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
- E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian)
- E. I. Vatutin, About the minimum number of intercalates in a diagonal Latin squares of order 9 (in Russian)
- E. 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, About the heuristic approximation of the spectrum of number of intercalates in diagonal Latin squares of order 14 (in Russian)
- Eduard I. Vatutin, About the minimum number of intercalates in diagonal Latin squares of order 15 (in Russian)
- E. Vatutin, A. Belyshev, N. Nikitina, and M. Manzuk, Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10, Communications in Computer and Information Science, Vol. 1304, Springer, 2020, pp. 127-146, DOI: 10.1007/978-3-030-66895-2_9.
- E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian)
- Eduard I. Vatutin, Proving list (best known examples).
- Index entries for sequences related to Latin squares and rectangles.
A307166
Minimum number of loops in a diagonal Latin square of order n.
Original entry on oeis.org
1, 0, 0, 12, 10, 27, 21, 40
Offset: 1
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.
The total number of loops for this square is 21.
- 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 loops in a diagonal Latin squares of order 8 (in Russian).
- E. 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 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.
A307171
Maximum number of partial loops in a diagonal Latin square of order n.
Original entry on oeis.org
0, 0, 0, 12, 8, 21, 53, 112
Offset: 1
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.
- 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 partial loops 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.
Showing 1-3 of 3 results.
Comments