A279849 - OEIS

%I #11 Feb 16 2025 08:33:38

%S 1,2,3,4,3,4,1,2,4,3,2,1,2,1,4,3,1,2,3,4,4,3,2,1,2,1,4,3,3,4,1,2,1,2,

%T 4,3,3,4,2,1,2,1,3,4,4,3,1,2,1,2,4,3,4,3,1,2,3,4,2,1,2,1,3,4,1,3,2,4,

%U 2,4,1,3,4,2,3,1,3,1,4,2,1,3,2,4,4,2,3,1,3,1,4,2,2,4,1,3

%N Rows of the 48 self-orthogonal Latin squares of order 4, 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.

%H Colin Barker, <a href="/A279849/b279849.txt">Table of n, a(n) for n = 1..768</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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 few squares are:

%e 1 2 3 4   1 2 3 4   1 2 4 3   1 2 4 3   1 3 2 4   1 3 2 4   1 3 4 2

%e 3 4 1 2   4 3 2 1   3 4 2 1   4 3 1 2   2 4 1 3   4 2 3 1   2 4 3 1

%e 4 3 2 1   2 1 4 3   2 1 3 4   3 4 2 1   4 2 3 1   3 1 4 2   3 1 2 4

%e 2 1 4 3   3 4 1 2   4 3 1 2   2 1 3 4   3 1 4 2   2 4 1 3   4 2 1 3

%Y Cf. A160368, A279648, A279649, A279650, A279850.

%K nonn,fini,full,tabf

%O 1,2

%A _Colin Barker_, Dec 20 2016