A385034 Absolute value squared of the maximal determinant of a matrix of order n with entries in the third roots of unity.

1, 1, 3, 27, 189, 1701, 46656, 606528, 8957952, 387420489, 7360989291, 154580775111, 8916100448256, 222902511206400

Offset: 0

Author

Guillermo N. Ponasso, Jun 16 2025

Keywords

• nonn
• hard
• more

Comments

The n-th term is equal to n^n if and only if a Butson-type Hadamard matrix over the third roots exist.

Examples

			With w=exp(2*Pi*i/3) and i the imaginary unit, a matrix corresponding to a(3) = 27 is
  [1, 1,   1;
   1, w,   w^2;
   1, w^2, w],
and a matrix corresponding to a(4) = 189 is
  [w, 1, 1, 1;
   1, w, 1, 1;
   1, 1, w, 1;
   1, 1, 1, w].
		

Links

• G. Nuñez Ponasso, Maximal determinants of matrices over the roots of unity, Linear Algebra and its Applications, 723 (2025), 201-243.

Crossrefs

Cf. A000312, A003433.