cp's OEIS Frontend

A309985 Maximum determinant of an n X n Latin square.

%I A309985 #68 Dec 12 2020 06:31:38
%S A309985 1,1,3,18,160,2325,41895,961772,26978400,929587995
%N A309985 Maximum determinant of an n X n Latin square.
%C A309985 a(n) = A301371(n) for n <= 7. a(8) < A301371(8) = 27296640, a(9) < A301371(9) = 933251220.
%C A309985 a(10) = 36843728625, conjectured. See Stack Exchange link. - _Hugo Pfoertner_, Sep 29 2019
%C A309985 A328030(n) <= a(n) <= A301371(n). - _Hugo Pfoertner_, Dec 02 2019
%C A309985 It is unknown, but very likely, that A301371(n) > a(n) also holds for all n > 9 - _Hugo Pfoertner_, Dec 12 2020
%H A309985 Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin squares</a>.
%H A309985 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/885481/maximum-determinant-of-latin-squares">Maximum determinant of Latin squares</a>, (2014), (2016).
%e A309985 An example of an 8 X 8 Latin square with maximum determinant is
%e A309985   [7  1  3  4  8  2  5  6]
%e A309985   [1  7  4  3  6  5  2  8]
%e A309985   [3  4  1  7  2  6  8  5]
%e A309985   [4  3  7  1  5  8  6  2]
%e A309985   [8  6  2  5  4  7  1  3]
%e A309985   [2  5  6  8  7  3  4  1]
%e A309985   [5  2  8  6  1  4  3  7]
%e A309985   [6  8  5  2  3  1  7  4].
%e A309985 An example of a 9 X 9 Latin square with maximum determinant is
%e A309985   [9  4  3  8  1  5  2  6  7]
%e A309985   [3  9  8  5  4  6  1  7  2]
%e A309985   [4  1  9  3  2  8  7  5  6]
%e A309985   [1  2  4  9  7  3  6  8  5]
%e A309985   [8  3  5  6  9  7  4  2  1]
%e A309985   [2  7  1  4  6  9  5  3  8]
%e A309985   [5  8  6  7  3  2  9  1  4]
%e A309985   [7  6  2  1  5  4  8  9  3]
%e A309985   [6  5  7  2  8  1  3  4  9].
%e A309985 An example of a 10 X 10 Latin square with abs(determinant) = 36843728625 is a circulant matrix with first row [1, 3, 7, 9, 8, 6, 5, 4, 2, 10], but it is not known if this is the best possible. - _Kebbaj Mohamed Reda_, Nov 27 2019 (reworded by _Hugo Pfoertner_)
%Y A309985 Cf. A040082, A301371, A308853, A309258, A309984, A328029, A328030.
%K A309985 nonn,hard,more
%O A309985 0,3
%A A309985 _Hugo Pfoertner_, Aug 26 2019
%E A309985 a(9) from _Hugo Pfoertner_, Aug 30 2019
%E A309985 a(0)=1 prepended by _Alois P. Heinz_, Oct 02 2019