cp's OEIS Frontend

In A098072 an example of a 3 X 3 matrix was shown that produces the maximum number A088021(3)=10080 of distinct determinants when all permutations of the given matrix entries are performed under the condition of minimizing the greatest entry of the matrix. The current sequence improves this result, i.e., the maximum is reduced from 100 to 99. It is optimal under the assumptions that the matrix entries are distinct and that the two smallest entries are 0 and 1.

The resulting determinant values are given in A301757.

The nonexistence of solutions with maximum matrix element < 94 was proved by exhaustive search.

For large values of n it is always possible to find a matrix that produces A088021(3)=10080 different determinants. Examples are given in the link. Currently (October 2004) the smallest known n for which a(n)=10080 is 100. The elements of the corresponding matrix are given in A098072.