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

%I #20 Jun 04 2023 01:45:31

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

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

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

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

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

%C 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.

%H Arun et al., <a href="https://mathoverflow.net/q/418009">Reference request: maximal determinant of matrices with pairwise orthogonal rows and entries in {1, 0, -1}</a>, MathOverflow, 2022.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Conference_matrix">Conference matrix</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hadamard_matrix">Hadamard matrix</a>.

%Y Cf. A000952, A003432, A003433.

%K hard,more,nonn

%O 1,2

%A _Max Alekseyev_, Mar 12 2022

%E a(11)-a(14) from _Max Alekseyev_, May 20 2023