login
A279850
Rows of the 1440 self-orthogonal Latin squares of order 5, lexicographically sorted.
5
1, 2, 3, 4, 5, 3, 4, 2, 5, 1, 4, 1, 5, 3, 2, 5, 3, 1, 2, 4, 2, 5, 4, 1, 3, 1, 2, 3, 4, 5, 3, 4, 5, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1, 4, 5, 1, 2, 3, 1, 2, 3, 4, 5, 3, 5, 2, 1, 4, 5, 1, 4, 2, 3, 2, 4, 5, 3, 1, 4, 3, 1, 5, 2, 1, 2, 3, 4, 5, 3, 5, 4, 2, 1, 4, 1, 2, 5, 3, 5, 4, 1, 3, 2, 2, 3, 5, 1, 4
OFFSET
1,2
COMMENTS
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.
Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.
LINKS
Eric Weisstein's World of Mathematics, Latin square
Wikipedia, Latin square
EXAMPLE
The first few squares are:
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
3 4 2 5 1 3 4 5 1 2 3 5 2 1 4 3 5 4 2 1 4 3 1 5 2 4 3 5 2 1
4 1 5 3 2 5 1 2 3 4 5 1 4 2 3 4 1 2 5 3 2 4 5 3 1 5 4 2 1 3
5 3 1 2 4 2 3 4 5 1 2 4 5 3 1 5 4 1 3 2 5 1 4 2 3 3 1 4 5 2
2 5 4 1 3 4 5 1 2 3 4 3 1 5 2 2 3 5 1 4 3 5 2 1 4 2 5 1 3 4
CROSSREFS
KEYWORD
nonn,fini,full,tabf
AUTHOR
Colin Barker, Dec 20 2016
STATUS
approved