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Encyclopaedia of DesignTheory: MOLS |
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Here is an example, where we have used A,B,C as symbols in one square and a,b,c in the other, and then superimposed the two squares for convenience.
Aa | Bb | Cc |
Bc | Ca | Ab |
Cb | Ac | Ba |
In this situation, one could use different alphabets (e.g. Latin and Greek) for the symols in the two squares. For this reason, a pair of orthogonal Latin squares is sometimes called a Graeco-Latin square.
A family of s Latin squares of order n is mutually orthogonal if any two squares in the family are orthogonal. We use the abbreviation MOLS for "mutually orthogonal Latin squares", and speak of s MOLS of order n, for example.
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Peter J. Cameron
16 April 2002