A299784
Maximum size of a main class for diagonal Latin squares of order n with the first row in ascending order.
Original entry on oeis.org
1, 0, 0, 2, 4, 96, 192, 1536, 1536, 15360, 15360, 184320, 184320, 2580480, 2580480
Offset: 1
From _Eduard I. Vatutin_, May 30 2021: (Start)
The following DLS of order 9 has a main class with cardinality 1536:
0 1 2 3 4 5 6 7 8
1 2 0 4 8 6 5 3 7
7 4 5 8 0 3 2 6 1
5 8 7 6 1 0 3 2 4
8 0 3 2 7 1 4 5 6
3 7 8 5 6 4 1 0 2
6 3 1 7 5 2 8 4 0
2 6 4 0 3 8 7 1 5
4 5 6 1 2 7 0 8 3
The following DLS of order 10 has a main class with cardinality 15360:
0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 3 9 8 6 7
3 5 6 1 8 7 4 0 9 2
9 4 7 8 3 2 1 6 0 5
2 7 3 0 9 8 5 1 4 6
6 8 5 9 2 4 7 3 1 0
4 6 9 7 0 1 3 2 5 8
7 0 4 6 1 9 8 5 2 3
8 3 1 5 6 0 2 9 7 4
5 9 8 2 7 6 0 4 3 1
(End)
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, and N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, and N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586.
- E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian).
- E. I. Vatutin, About the maximal size of main class for diagonal Latin squares of orders 11-15 (in Russian).
- Eduard I. Vatutin, Estimating the maximal size of main class for diagonal Latin squares of orders 9-15, Medical-Ecological and Information Technologies - 2020, Part 2, 2020, pp. 57-62. (in Russian)
- Eduard I. Vatutin, About the relationship between the minimal and maximal cardinality of main classes for diagonal Latin squares (in Russian).
- Eduard I. Vatutin, Proving list (best known examples).
- Index entries for sequences related to Latin squares and rectangles.
A299787
Maximum size of a main class for diagonal Latin squares of order n.
Original entry on oeis.org
1, 0, 0, 48, 480, 69120, 967680, 61931520, 557383680, 55738368000, 613122048000, 88289574912000, 1147764473856000, 224961836875776000, 3374427553136640000
Offset: 1
From _Eduard I. Vatutin_, May 31 2021: (Start)
The following DLS of order 9 has a main class with cardinality 1536*9! = 557383680:
0 1 2 3 4 5 6 7 8
1 2 0 4 8 6 5 3 7
7 4 5 8 0 3 2 6 1
5 8 7 6 1 0 3 2 4
8 0 3 2 7 1 4 5 6
3 7 8 5 6 4 1 0 2
6 3 1 7 5 2 8 4 0
2 6 4 0 3 8 7 1 5
4 5 6 1 2 7 0 8 3
The following DLS of order 10 has a main class with cardinality 15360*10! = 55738368000:
0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 3 9 8 6 7
3 5 6 1 8 7 4 0 9 2
9 4 7 8 3 2 1 6 0 5
2 7 3 0 9 8 5 1 4 6
6 8 5 9 2 4 7 3 1 0
4 6 9 7 0 1 3 2 5 8
7 0 4 6 1 9 8 5 2 3
8 3 1 5 6 0 2 9 7 4
5 9 8 2 7 6 0 4 3 1
(End)
- E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian).
- E. I. Vatutin, About the maximal size of main classes of diagonal Latin squares of orders 9 and 10 (in Russian).
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586.
- E. I. Vatutin, About the maximal size of main class for diagonal Latin squares of orders 11-15 (in Russian).
- Eduard I. Vatutin, About the relationship between the minimal and maximal cardinality of main classes for diagonal Latin squares (in Russian).
- Eduard I. Vatutin, Estimating the maximal size of main class for diagonal Latin squares of orders 9-15, Medical-Ecological and Information Technologies - 2020, Part 2, 2020, pp. 57-62 (in Russian).
- Eduard I. Vatutin, Proving list (best known examples).
- Index entries for sequences related to Latin squares and rectangles.
A299785
Minimum size of a main class for diagonal Latin squares of order n.
Original entry on oeis.org
1, 0, 0, 48, 480, 23040, 161280, 3870720
Offset: 1
From _Eduard I. Vatutin_, Oct 05 2020: (Start)
The following DLS of order 9 has a main class with cardinality 48*9! = 17418240:
0 1 2 3 4 5 6 7 8
2 4 3 0 7 6 8 1 5
6 2 8 5 3 4 7 0 1
4 6 7 1 8 2 3 5 0
1 5 4 7 6 0 2 8 3
7 8 1 4 5 3 0 6 2
3 7 0 2 1 8 5 4 6
8 3 5 6 0 7 1 2 4
5 0 6 8 2 1 4 3 7
The following DLS of order 10 has a main class with cardinality 7680*10! = 27869184000:
0 1 2 3 4 5 6 7 8 9
1 2 0 4 3 6 5 9 7 8
2 0 3 5 8 1 4 6 9 7
4 6 9 7 1 8 2 0 3 5
9 7 8 6 5 4 3 1 2 0
3 4 7 8 0 9 1 2 5 6
6 9 4 1 7 2 8 5 0 3
7 8 5 0 6 3 9 4 1 2
5 3 1 9 2 7 0 8 6 4
8 5 6 2 9 0 7 3 4 1
(End)
- E. I. Vatutin, Discussion about properties of diagonal Latin squares at forum.boinc.ru (in Russian).
- E. I. Vatutin, About the upper bound of the minimal size of main class for diagonal Latin squares of order 9 (in Russian).
- E. I. Vatutin, About the upper bound of the minimal size of main class for diagonal Latin squares of order 10 (in Russian).
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
- E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586.
- Eduard I. Vatutin, About the relationship between the minimal and maximal cardinality of main classes for diagonal Latin squares (in Russian).
- Eduard I. Vatutin, Proving list (best known examples).
- Index entries for sequences related to Latin squares and rectangles.
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