A099834 -id:A099834 - cp's OEIS frontend

A099815 Maximum determinant that can be formed from the optimal set of nonnegative 3 X 3 matrix elements <=n, which maximize the number of different determinants given in A099834.

2, 7, 28, 62, 123, 202, 331, 456, 724, 937, 1391, 1526, 2084, 2424, 3107, 3771, 4694, 5704, 7119, 8062, 9632, 10987, 12332, 14506, 16626, 19296, 22492, 21669, 25179, 27430, 32044, 32555, 39916, 41032

Offset: 1

Hugo Pfoertner, Nov 19 2004

If more than one set of optimal matrix elements exists then the set producing the smallest maximum is selected. This occurs for n=2, where 3 different sets of matrix elements allow the construction of 15 different determinants. {2 2 2 1 1 1 1 0 0} produces the smallest maximum a(2)=7. Other examples are n=5 and n=41 (a(41)=77902).

			a(3)=28 because the largest determinant (of A099834(3)=53 possible different determinants) of a matrix using the elements of the optimal set {3 3 3 2 2 1 1 0 0} is det((3,2,0),(0,3,1),(2,1,3))=28.

Cf. A099834.

A098072 An example of a 3 X 3 matrix with nonnegative elements that produces the maximum possible number of 10080 different determinants if all 9! permutations of the matrix elements are performed. The target is to find a matrix for which the largest element becomes as small as possible.

Original entry on oeis.org

0, 1, 17, 43, 82, 87, 88, 91, 100

Offset: 1

Hugo Pfoertner, Nov 19 2004

In November 2004 this is the example with the smallest known largest element. It was found in a random search after 3 CPU (1.5 GHz Intel Itanium 2) months. No improvement was found in another 6 months of CPU time.

Hugo Pfoertner, List of 3 X 3 integer matrices that give 10080 different determinants.
Hugo Pfoertner, Search minimal 3 X 3 matrix with 10080 different determinants. FORTRAN program.

Cf. A088021 maximal number of different determinants of an n X n matrix, A099834 different determinants of matrix with nonnegative entries <=n.
Improved solution: A301372.
Optimal solution found by exhaustive search: A316601.

Fortran
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cp's OEIS Frontend

A099815 Maximum determinant that can be formed from the optimal set of nonnegative 3 X 3 matrix elements <=n, which maximize the number of different determinants given in A099834.

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