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

1,2

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

Table of n, a(n) for n=1..14.

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.

Sequence in context: A016740 A353915 A193145 * A133922 A222954 A240033

Adjacent sequences: A352345 A352346 A352347 * A352349 A352350 A352351

Keyword

hard,more,nonn

Author

Max Alekseyev, Mar 12 2022

Extensions

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

Status

approved