Graeco-Latin square | Graeco-Roman square | Latin-Graeco 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.

Latin rectangle | Latin square | room square