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Euler Square


A square array made by combining n objects of two types such that the first and second elements form Latin squares. Euler squares are also known as Graeco-Latin squares, Graeco-Roman squares, or Latin-Graeco squares.

For many years, Euler squares were known to exist for n=3, 4, and for every odd n except n=3k. Euler's Graeco-roman squares conjecture maintained that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... However, such squares were found to exist in 1959, refuting the conjecture. As of 1959, Euler squares are known to exist for all n except n=2 and n=6.


See also

Latin Rectangle, Latin Square, Room Square

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References

Beezer, R. "Graeco-Latin Squares." http://buzzard.ups.edu/squares.html.Fisher, R. A. The Design of Experiments, 8th ed. New York: Hafner, 1971.Kraitchik, M. "Euler (Graeco-Latin) Squares." §7.12 in Mathematical Recreations. New York: W. W. Norton, pp. 179-182, 1942.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 31-33, 1999.

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Euler Square

Cite this as:

Weisstein, Eric W. "Euler Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerSquare.html

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