A301372 -id:A301372 - cp's OEIS frontend

A301757 Positive determinant values assumed by performing all permutations of entries in the 3 X 3 matrix of A301372.

27, 147, 168, 171, 197, 293, 317, 331, 332, 408, 441, 469, 532, 547, 568, 643, 717, 819, 845, 901, 909, 971, 1017, 1028, 1080, 1104, 1182, 1201, 1297, 1388, 1392, 1400, 1423, 1591, 1606, 1624, 1633, 1640, 1846, 1891, 2038, 2042, 2089, 2114, 2275, 2278, 2288, 2369, 2384

Offset: 1

Hugo Pfoertner, Mar 26 2018

A 3 X 3 matrix with given 9 matrix entries can produce A088021(3)=10080 distinct determinants if all positional permutations are performed. The current sequence provides the 5040 positive determinants of a conjectured optimal matrix minimizing its greatest matrix entry.

			a(1) = 27 because the smallest determinant that can be achieved from the matrix entries of A301372 is
det (( 0  1 89)
     (87 99 97)
     (54 61 20)) = 27,
.
a(5040) = 1039208:
det ((99 54  1)
     (20 97 87)
     (61  0 89)) = 1039208.

Hugo Pfoertner, Table of n, a(n) for n = 1..5040
Hugo Pfoertner, Determinant values plotted as CDF.

Cf. A088021, A301372.

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.

Original entry on oeis.org

0, 1, 17, 43, 82, 87, 88, 91, 100

Offset: 1

Hugo Pfoertner, Nov 19 2004

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.

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.

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.

Fortran
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! See Links section.
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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

A301757 Positive determinant values assumed by performing all permutations of entries in the 3 X 3 matrix of A301372.

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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.

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Fortran

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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