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

Author

Colin Barker, Dec 16 2016

Keywords

• nonn
• fini
• full
• 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.

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

Examples

			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
		

Links

• Eric Weisstein's World of Mathematics, Latin square
• Wikipedia, Latin square

Crossrefs

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