A098072 - OEIS

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

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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