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A358325 a(n) is the minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 0 to n - 1. 4
1, 3, 12, 2, 11, 10, 5, 4, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
LINKS
Lucas A. Brown, Python program.
Wikipedia, Toeplitz Matrix
EXAMPLE
a(3) = 3:
[1, 0, 2;
0, 1, 0;
2, 0, 1]
a(4) = 12:
[3, 2, 1, 0;
2, 3, 2, 1;
1, 2, 3, 2;
0, 1, 2, 3]
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]
MATHEMATICA
Table[Min[Select[Table[Abs[Det[ToeplitzMatrix[Part[Permutations[Join[{0}, Range[n-1]]], i]]]], {i, n!}], Positive]], {n, 2, 9}] (* Corrected by Stefano Spezia, Nov 17 2022 *)
CROSSREFS
Cf. A356865.
Cf. A358323 (minimal signed), A358324 (maximal signed), A358326 (minimal permanent), A358327 (maximal permanent).
Sequence in context: A342787 A110121 A321710 * A288518 A069522 A170857
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia, Nov 09 2022
EXTENSIONS
a(3), a(7), and a(10)-a(12) from Lucas A. Brown, Nov 16 2022
STATUS
approved

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Last modified February 28 08:48 EST 2024. Contains 370394 sequences. (Running on oeis4.)