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.

1, 1, 3, 9, 16, 21, 20, 17, 131, 62, 1

Offset: 0

Author

Stefano Spezia, Jan 21 2023

Keywords

• nonn
• hard
• more

Examples

			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 ]
		

Links

• Wikipedia, Toeplitz Matrix

Crossrefs

Cf. A348891, A358325.

Cf. A359559, A359561.

Cf. A359614 (minimal signed), A359615 (maximal signed), A359616 (minimal permanent), A359617 (maximal permanent).

Programs

Mathematica

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]]]]])