Euler Square

A square Array made by combining objects of two types such that the first and second elements form LatinSquares. 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 , 4, and for every Odd except . Euler's Graeco-Roman SquaresConjecture maintained that there do not exist Euler squares of order for , 2, .... However, such squares werefound to exist in 1959, refuting the Conjecture.

References

Beezer, R. ``Graeco-Latin Squares.'' http://buzzard.ups.edu/squares.html.

Kraitchik, M. ``Euler (Graeco-Latin) Squares.'' §7.12 in Mathematical Recreations. New York: W. W. Norton, pp. 179-182, 1942.

• Ordered Pair
• Ordered Tree
• Order (Field)
• Order (Group)
• Ordering
• Ordering Axioms
• Order (Modulo)
• Order (Ordinary Differential Equation)
• Order (Permutation)
• Order (Polynomial)
• Order Statistic
• Order (Vertex)
• Ordinal Number
• Ordinary Differential Equation
• Ordinary Differential Equation--First-Order
• Ordinary Differential Equation--First-Order Exact
• Ordinary Differential Equation Second-Order
• Ordinary Differential Equation--System with Constant Coefficients
• Ordinary Double Point
• Ordinary Line
• Ordinary Point
• Ordinate
• Ore Number
• Ore's Conjecture
• Ore's Theorem