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:

Title	Graeco-Latin squares
Canonical name	GraecoLatinSquares
Date of creation	2013-03-22 12:14:36
Last modified on	2013-03-22 12:14:36
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	9
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 05B15
Defines	join