Definition:Graeco-Latin Square
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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