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

Author

Hugo Pfoertner, Nov 19 2004

Keywords

• fini
• full
• nonn

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

• 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.

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.

Programs

Fortran

! See Links section.