A301757 -id:A301757 - cp's OEIS frontend

A301372 Conjectured best solution for the problem stated in A098072.

0, 1, 20, 54, 61, 87, 89, 97, 99

Offset: 1

Hugo Pfoertner, Mar 26 2018

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.

Cf. A088021, A098072, A301757.

A316601 Optimal solution for the problem stated in A098072.

Original entry on oeis.org

0, 3, 19, 65, 75, 83, 88, 93, 94

Offset: 1

Hugo Pfoertner, Jul 13 2018

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

Cf. A088021, A098072, A301372, A301757, A316602.

A316602 Positive determinant values assumed by performing all permutations of entries in the 3 X 3 matrix of A316601.

Original entry on oeis.org

1, 9, 29, 67, 162, 267, 309, 430, 452, 520, 570, 712, 716, 825, 841, 844, 941, 943, 980, 1120, 1287, 1289, 1396, 1478, 1516, 1521, 1580, 1592, 1605, 1700, 1753, 1870, 1875, 1914, 1950, 1989, 2157, 2245, 2254, 2265

Offset: 1

Hugo Pfoertner, Jul 17 2018

			a(1) = 1 because the smallest determinant that can be achieved from the matrix entries of A316601 is
det (( 0  3 19)
     (94 88 93)
     (83 75 65)) = 1,
.
a(5040) = 1039208:
det ((88  3 83)
     (75 94 19)
     ( 0 65 93)) = 1044316.

Hugo Pfoertner, Table of n, a(n) for n = 1..5040

Cf. A088021, A301372, A301757, A316601.

cp's OEIS Frontend

A301372 Conjectured best solution for the problem stated in A098072.

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A316601 Optimal solution for the problem stated in A098072.

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A316602 Positive determinant values assumed by performing all permutations of entries in the 3 X 3 matrix of A316601.

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