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%I #12 Dec 21 2016 13:49:06
%S 1,2,3,4,5,6,7,8,3,4,1,2,6,5,8,7,4,5,7,3,8,2,1,6,6,7,5,8,3,1,2,4,7,1,
%T 4,6,2,8,5,3,5,8,6,7,1,3,4,2,8,3,2,5,4,7,6,1,2,6,8,1,7,4,3,5,1,2,3,4,
%U 5,6,7,8,3,4,1,2,6,5,8,7,4,5,8,3,7,2,6,1,6,8,5,7,3,1,4,2,8,1,4,6,2,7,3,5,5,7,6,8,1,3,2,4,2,6,7,1,8,4,5,3,7,3,2,5,4,8,1,6
%N Rows of the self-orthogonal Latin squares of order 8, lexicographically sorted.
%C An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.
%C Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
%C A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
%C There are 4180377600 self-orthogonal Latin squares of order 8.
%H Colin Barker, <a href="/A279649/b279649.txt">Table of n, a(n) for n = 1..750</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatinSquare.html">Latin square</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Latin_square">Latin square</a>
%e The first four squares are:
%e 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
%e 3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7 3 4 1 2 6 5 8 7
%e 4 5 7 3 8 2 1 6 4 5 8 3 7 2 6 1 4 6 7 3 2 8 1 5 4 6 8 3 2 7 5 1
%e 6 7 5 8 3 1 2 4 6 8 5 7 3 1 4 2 5 7 6 8 1 3 2 4 5 8 6 7 1 3 4 2
%e 7 1 4 6 2 8 5 3 8 1 4 6 2 7 3 5 6 8 5 7 3 1 4 2 6 7 5 8 3 1 2 4
%e 5 8 6 7 1 3 4 2 5 7 6 8 1 3 2 4 7 1 4 5 8 2 6 3 8 1 4 5 7 2 3 6
%e 8 3 2 5 4 7 6 1 2 6 7 1 8 4 5 3 8 3 2 6 7 4 5 1 2 5 7 1 4 8 6 3
%e 2 6 8 1 7 4 3 5 7 3 2 5 4 8 1 6 2 5 8 1 4 7 3 6 7 3 2 6 8 4 1 5
%Y Cf. A160368, A279648, A279650, A279849, A279850.
%K nonn,fini,tabf
%O 1,2
%A _Colin Barker_, Dec 16 2016
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