A279850 - OEIS

A279850

Rows of the 1440 self-orthogonal Latin squares of order 5, lexicographically sorted.

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

(list; graph; refs; listen; history; text; internal format)

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

Colin Barker, Table of n, a(n) for n = 1..36000

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

Cf. A160368, A279648, A279649, A279650, A279849.

Sequence in context: A341355 A104413 A127064 * A117607 A215092 A345018

Adjacent sequences: A279847 A279848 A279849 * A279851 A279852 A279853

KEYWORD

nonn,fini,full,tabf

AUTHOR

Colin Barker, Dec 20 2016

STATUS

approved

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