A279650 An idempotent self-orthogonal Latin square of order 11, read by rows.

1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11

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.

An m X m self-orthogonal Latin square is idempotent if the diagonal contains 1 to m in order.

Links

Table of n, a(n) for n=1..121.

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

Example

The Latin square is:
   1 11 10  9  8  7  6  5  4  3  2
   3  2  1 11 10  9  8  7  6  5  4
   5  4  3  2  1 11 10  9  8  7  6
   7  6  5  4  3  2  1 11 10  9  8
   9  8  7  6  5  4  3  2  1 11 10
  11 10  9  8  7  6  5  4  3  2  1
   2  1 11 10  9  8  7  6  5  4  3
   4  3  2  1 11 10  9  8  7  6  5
   6  5  4  3  2  1 11 10  9  8  7
   8  7  6  5  4  3  2  1 11 10  9
  10  9  8  7  6  5  4  3  2  1 11

Crossrefs

Cf. A160368, A279648, A279649, A279849, A279850.

Sequence in context: A023453 A261304 A055122 * A004452 A291467 A112952

Adjacent sequences: A279647 A279648 A279649 * A279651 A279652 A279653

Keyword

nonn,fini,full,tabf

Author

Colin Barker, Dec 16 2016

Status

approved