A279649 Rows of the self-orthogonal Latin squares of order 8, lexicographically sorted.

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, 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, 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

Offset: 1

Author

Colin Barker, Dec 16 2016

Keywords

• nonn
• fini
• tabf

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.

There are 4180377600 self-orthogonal Latin squares of order 8.

Examples

			The first four squares are:
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
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
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
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
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
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
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
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
		

Links

• Colin Barker, Table of n, a(n) for n = 1..750
• Eric Weisstein's World of Mathematics, Latin square
• Wikipedia, Latin square

Crossrefs

Cf. A160368, A279648, A279650, A279849, A279850.