A358323
a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
Original entry on oeis.org
1, 0, -1, -7, -60, -1210, -34020, -607332, -30448441, -1093612784, -55400732937, -2471079070511, -197500419383964
Offset: 0
a(3) = -7:
[1, 2, 0;
2, 1, 2;
0, 2, 1]
a(4) = -60:
[2, 3, 0, 1;
3, 2, 3, 0;
0, 3, 2, 3;
1, 0, 3, 2]
a(5) = -1210:
[4, 3, 0, 2, 1;
3, 4, 3, 0, 2;
0, 3, 4, 3, 0;
2, 0, 3, 4, 3;
1, 2, 0, 3, 4]
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Join[{1}, Table[Min[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]
A358324
a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n - 1.
Original entry on oeis.org
1, 0, 1, 8, 63, 2090, 36875, 1123653, 34292912, 1246207300, 53002204560, 2418538080316, 215120941720912
Offset: 0
a(3) = 8:
[0, 2, 1;
2, 0, 2;
1, 2, 0]
a(4) = 63:
[1, 3, 2, 0;
3, 1, 3, 2;
2, 3, 1, 3;
0, 2, 3, 1]
a(5) = 2090:
[2, 4, 0, 1, 3;
4, 2, 4, 0, 1;
0, 4, 2, 4, 0;
1, 0, 4, 2, 4;
3, 1, 0, 4, 2]
-
Join[{1}, Table[Max[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]],{i,n!}]],{n,9}]]
A369834
a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix using the integers 0 to n-1.
Original entry on oeis.org
1, 1, 2, 5, 23, 94, 614, 4628, 38243, 351024
Offset: 0
-
a[n_] := CountDistinct[Table[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n - 1]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
-
from itertools import permutations
from sympy import Matrix
def A369834(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).det() for p in permutations(range(n))}) # Chai Wah Wu, Feb 11 2024
A374282
a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 4, 12, 2, 13, 16, 21, 4, 1
Offset: 2
a(5) = 2:
[0, 4, 1, 2, 3]
[4, 0, 4, 1, 2]
[1, 4, 0, 4, 1]
[2, 1, 4, 0, 4]
[3, 2, 1, 4, 0]
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a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,9,2]
A359618
a(n) is the minimal absolute value of the determinant of a nonsingular n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with off-diagonal elements purely imaginary.
Original entry on oeis.org
1, 1, 3, 9, 16, 21, 20, 17, 131, 62, 1
Offset: 0
a(4) = 16:
[ 1, 2*i, 4*i, 3*i;
-2*i, 1, 2*i, 4*i;
-4*i, -2*i, 1, 2*i;
-3*i, -4*i, -2*i, 1 ]
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a={1}; For[n=1, n<=8, n++, mn=Infinity; For[d=1, d<=n, d++, For[i=1, i<=(n-1)!, i++, If[0<(t=Abs[Det[ToeplitzMatrix[Join[{d}, I Part[Permutations[Drop[Range[n], {d}]], i]]]]])
Showing 1-5 of 5 results.
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