# Graeco-Latin squares

Let $A=(a_{ij})$ and $B=(b_{ij})$ be two $n\times n$ matrices. We define their as the matrix whose $(i,j)$th entry is the pair $(a_{ij},b_{ij})$.

A Graeco-Latin square is then the join of two Latin squares.

The name comes from Euler’s use of Greek and Latin letters to differentiate the entries on each array.

An example of Graeco-Latin square:

 $\begin{pmatrix}a\alpha&b\beta&c\gamma&d\delta\\ d\gamma&c\delta&b\alpha&a\beta\\ b\delta&a\gamma&d\beta&c\alpha\\ c\beta&d\alpha&a\delta&b\gamma\end{pmatrix}$
Title Graeco-Latin squares GraecoLatinSquares 2013-03-22 12:14:36 2013-03-22 12:14:36 Mathprof (13753) Mathprof (13753) 9 Mathprof (13753) Definition msc 05B15 join