GraecoLatin squares
are nicely illustrated in Rob Beezer's page (University of Puget Sound).
Cuttheknot.com has an applet that leads you through the construction of a latin
square: any suitable beginning can always be completed. An experimental
latin square design
and analysis is given on the site of the Washington State University
Tree Fruit Research and Extension Center. A contemporary agricultural
experiment with latin square design is
Effect of Magnesium and Sulfur Fertilization of Alfalfa by K. L. Wells
and J. E. Dollarhide, University of Kentucky.
Examples:
A  B 
B  A 
is a 2 x 2 latin square. The name comes from the elements usually being represented, as they are here, by letters of the Latin alphabet (this terminology goes back to Euler).
A  B  C 
B  C  A 
C  A  B 
is a 3 x 3 latin square, and this pattern can be extended to any size.
A a  B b  C c 
B c  C a  A b 
C b  A c  B a 
is a 3 x 3 example, but there is no example of size 2, as is easy to check.
They also have attracted the attention of mathematicians since Euler, who conjectured that there was no graecolatin square of size 2 plus a multiple of 4. He was right for 2 and 6, but wrong otherwise.
This is the first of two columns on this topic. Here we will look at the application of latin squares to statistics. The next column will look at some aspects of their mathematical study.
Tony Phillips
Stony Brook

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