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

1,2

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.

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

Links

Colin Barker, Table of n, a(n) for n = 1..750

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

Example

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

Crossrefs

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

Sequence in context: A043268 A346973 A238593 * A278060 A160597 A327389

Adjacent sequences: A279646 A279647 A279648 * A279650 A279651 A279652

Keyword

nonn,fini,tabf

Author

Colin Barker, Dec 16 2016

Status

approved