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A279648 Rows of the self-orthogonal Latin squares of order 7, lexicographically sorted.

%I A279648 #14 Feb 16 2025 08:33:38
%S A279648 1,2,3,4,5,6,7,3,4,2,5,6,7,1,4,7,6,3,1,2,5,6,1,5,7,2,4,3,2,5,7,6,3,1,
%T A279648 4,7,3,1,2,4,5,6,5,6,4,1,7,3,2,1,2,3,4,5,6,7,3,4,2,5,6,7,1,5,1,6,7,3,
%U A279648 4,2,6,7,1,3,2,5,4,2,5,4,6,7,1,3,7,3,5,1,4,2,6,4,6,7,2,1,3,5
%N A279648 Rows of the self-orthogonal Latin squares of order 7, lexicographically sorted.
%C A279648 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 A279648 Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
%C A279648 A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
%C A279648 There are 19353600 self-orthogonal Latin squares of order 7.
%H A279648 Colin Barker, <a href="/A279648/b279648.txt">Table of n, a(n) for n = 1..500</a>
%H A279648 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LatinSquare.html">Latin square</a>
%H A279648 Wikipedia, <a href="http://en.wikipedia.org/wiki/Latin_square">Latin square</a>
%e A279648 The first four squares are:
%e A279648 1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7
%e A279648 3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1
%e A279648 4 7 6 3 1 2 5   5 1 6 7 3 4 2   5 7 6 1 3 2 4   5 7 6 1 3 2 4
%e A279648 6 1 5 7 2 4 3   6 7 1 3 2 5 4   6 1 7 2 4 3 5   6 1 7 3 2 4 5
%e A279648 2 5 7 6 3 1 4   2 5 4 6 7 1 3   2 5 1 3 7 4 6   2 5 4 6 7 1 3
%e A279648 7 3 1 2 4 5 6   7 3 5 1 4 2 6   7 3 4 6 1 5 2   7 3 1 2 4 5 6
%e A279648 5 6 4 1 7 3 2   4 6 7 2 1 3 5   4 6 5 7 2 1 3   4 6 5 7 1 3 2
%Y A279648 Cf. A160368, A279649, A279650, A279849, A279850.
%K A279648 nonn,fini,tabf
%O A279648 1,2
%A A279648 _Colin Barker_, Dec 16 2016