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.

1, 3, 12, 2, 11, 10, 5, 4, 1, 4, 1

Offset: 2

Author

Stefano Spezia, Nov 09 2022

Keywords

• nonn
• hard
• more

Examples

			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]
		

Links

• Lucas A. Brown, Python program.
• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A356865.

Cf. A358323 (minimal signed), A358324 (maximal signed), A358326 (minimal permanent), A358327 (maximal permanent).

Programs

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 *)

Extensions

a(3), a(7), and a(10)-a(12) from Lucas A. Brown, Nov 16 2022