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.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..9.

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.

Prog

FORTRAN program given at link.

Crossrefs

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.

Sequence in context: A328998 A031340 A172044 * A130467 A112885 A093191

Adjacent sequences: A098069 A098070 A098071 * A098073 A098074 A098075

Keyword

fini,full,nonn

Author

Hugo Pfoertner, Nov 19 2004

Status

approved