Definition:Graeco-Latin Square

Definition

A Graeco-Latin square is an amalgamation of $2$ orthogonal Latin squares into one.

This is conventionally (but not always) done by:

assigning one of the Latin squares to use Latin letters (that is, the conventional $\text A$ to $\text Z$)

assigning the other Latin squares to use lowercase Greek letters (that is, $\alpha$ to $\omega$).

In this way:

each Latin letter occurs once in each row and column

each Greek letter occurs once in each row and column

each Latin and Greek letter meet together in exactly one entry.

Examples

Order $3$

The following is an example of a Graeco-Latin square of order $3$:

$\begin{array} {|c|c|c|} \hline A \alpha & B \beta & C \gamma \\ \hline B \gamma & C \alpha & A \beta \\ \hline C \beta & A \gamma & B \alpha \\ \hline \end{array}$

Also see

• Results about Graeco-Latin squares can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Graeco-Latin square
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Graeco-Latin square