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Encyclopaedia of DesignTheory: MOLS

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Mutually orthogonal Latin squares

Two Latin squares L₁ and L₂ of order n are orthogonal if, for each pair (k,l) of symbols, there is a unique cell (i,j) in which L₁ has symbol k and L₂ has symbol l.

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

General	Partition	Incidence	Array
Experimental	Other designs	Math properties	Stat properties
Server	External	Bibliography	Miscellaneous