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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.

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0, 1, 17, 43, 82, 87, 88, 91, 100 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`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.`
	PROGRAM	`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.` `Sequence in context: A165981 A109998 A031340 this_sequence A130467 A112885 A093191` `Adjacent sequences: A098069 A098070 A098071 this_sequence A098073 A098074 A098075`
	KEYWORD	`fini,full,nonn`
	AUTHOR	`Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 19 2004`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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