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

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, 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, 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

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 19353600 self-orthogonal Latin squares of order 7.

Links

Colin Barker, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

Example

The first four squares are:
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
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
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
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
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
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
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

Crossrefs

Cf. A160368, A279649, A279650, A279849, A279850.

Sequence in context: A097449 A104415 A071074 * A066323 A245347 A278059

Adjacent sequences: A279645 A279646 A279647 * A279649 A279650 A279651

Keyword

nonn,fini,tabf

Author

Colin Barker, Dec 16 2016

Status

approved