A352348 Maximum determinant of n X n matrix composed of {-1, 0, 1} with pairwise orthogonal rows.

1, 2, 2, 16, 16, 125, 128, 4096, 4096, 59049, 59049, 2985984, 2985984, 62748517

Offset: 1

Author

Max Alekseyev, Mar 12 2022

Keywords

• hard
• more
• nonn

Comments

a(n) >= a(m)*a(n-m) for any m < n.

a(n) <= A003433(n), a bound achieved if the orthogonality requirement is dropped.

If there exists an order n Hadamard matrix, then a(n) = A003433(n) = n^(n/2).

For n == 2 (mod 4), if there exists an order n conference matrix (cf. A000952), then a(n) = (n-1)^(n/2). In particular, a(18) = 118587876497.

Links

• Arun et al., Reference request: maximal determinant of matrices with pairwise orthogonal rows and entries in {1, 0, -1}, MathOverflow, 2022.
• Wikipedia, Conference matrix.
• Wikipedia, Hadamard matrix.

Crossrefs

Cf. A000952, A003432, A003433.

Extensions

a(11)-a(14) from Max Alekseyev, May 20 2023