A309985
Maximum determinant of an n X n Latin square.
Original entry on oeis.org
1, 1, 3, 18, 160, 2325, 41895, 961772, 26978400, 929587995
Offset: 0
An example of an 8 X 8 Latin square with maximum determinant is
[7 1 3 4 8 2 5 6]
[1 7 4 3 6 5 2 8]
[3 4 1 7 2 6 8 5]
[4 3 7 1 5 8 6 2]
[8 6 2 5 4 7 1 3]
[2 5 6 8 7 3 4 1]
[5 2 8 6 1 4 3 7]
[6 8 5 2 3 1 7 4].
An example of a 9 X 9 Latin square with maximum determinant is
[9 4 3 8 1 5 2 6 7]
[3 9 8 5 4 6 1 7 2]
[4 1 9 3 2 8 7 5 6]
[1 2 4 9 7 3 6 8 5]
[8 3 5 6 9 7 4 2 1]
[2 7 1 4 6 9 5 3 8]
[5 8 6 7 3 2 9 1 4]
[7 6 2 1 5 4 8 9 3]
[6 5 7 2 8 1 3 4 9].
An example of a 10 X 10 Latin square with abs(determinant) = 36843728625 is a circulant matrix with first row [1, 3, 7, 9, 8, 6, 5, 4, 2, 10], but it is not known if this is the best possible. - _Kebbaj Mohamed Reda_, Nov 27 2019 (reworded by _Hugo Pfoertner_)
A328030
Maximum determinant of a circulant n X n matrix whose rows are permutations of [1,2,..,n].
Original entry on oeis.org
1, 1, 3, 18, 160, 2325, 41895, 961772, 26978400, 929587995, 36843728625, 1705290814194, 89802671542272, 5336424046419557, 354379732734283200, 26173529641406219400
Offset: 0
A328062
Lexicographically earliest permutation of [1,2,...,n] minimizing the positive value of the determinant of an n X n circulant matrix that uses this permutation as first row, written as triangle T(n,k), k <= n.
Original entry on oeis.org
1, 2, 1, 1, 2, 3, 3, 1, 4, 2, 1, 2, 4, 5, 3, 1, 2, 4, 5, 6, 3, 1, 2, 4, 6, 7, 5, 3, 3, 1, 5, 4, 8, 6, 7, 2, 1, 2, 4, 6, 8, 9, 7, 5, 3, 5, 1, 7, 3, 8, 4, 10, 6, 9, 2, 1, 2, 3, 8, 6, 4, 9, 10, 11, 5, 7, 3, 1, 5, 4, 9, 8, 12, 10, 11, 6, 7, 2, 1, 2, 3, 5, 8, 7, 6, 9, 11, 12, 13, 10, 4
Offset: 1
The triangle starts
1;
2, 1;
1, 2, 3;
3, 1, 4, 2;
1, 2, 4, 5, 3;
1, 2, 4, 5, 6, 3;
1, 2, 4, 6, 7, 5, 3;
3, 1, 5, 4, 8, 6, 7, 2;
1, 2, 4, 6, 8, 9, 7, 5, 3;
5, 1, 7, 3, 8, 4, 10, 6, 9, 2;
.
The 4th row of the triangle T(4,1)..T(4,4) = a(7)..a(10) is [3,1,4,2] because this is the lexicographically earliest permutation of [1,2,3,4] producing a circulant 4 X 4 matrix with minimum positive determinant A309257(4) = 80.
[3, 1, 4, 2;
2, 3, 1, 4;
4, 2, 3, 1;
1, 4, 2, 3].
All lexicographically earlier permutations lead to the other possible determinants -160, -80, 0, 160 with [1,3,2,4], [1,4,3,2], [2,3,1,4], and [2,4,1,3] producing determinants = -80.
Showing 1-3 of 3 results.
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