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Latin square - Wikipedia, the free encyclopedia
A Latin square is an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column. Here is an example:
begin{bmatrix} 1 & 2 & 3 \ 2 & 3 & 1 \ 3 & 1 & 2 \ end{bmatrix}

Latin squares occur as the multiplication tables (Cayley tables) of quasigroups. They have applications in the design of experiments and in error correcting codes.

The name Latin square originates from Leonhard Euler, who used Latin characters as symbols.

A Latin square is said to be reduced (also, normalized or in standard form) if its first row and first column are in natural order. For example, the Latin square above is reduced because both its first row and its first column are 1,2,3 (rather than 3,1,2 or any other order). We can make any Latin square reduced by permuting (reordering) the rows and columns.

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