6x1 Order-7 Latin Squares. Of these six Latin squares, the first and last are not pan-magic because their steps produce diagonal rows of letters. They are a related group. This will be important when we analyze the Fewest Representative Graeco-Latin Squares below. A Graeco-Latin square is made from a pair of orthogonal Latin squares.
Similar considerations apply to the second letter.
However, huge duplication is apparent when squares are reflected, rotated, and translocated. It is normalised by reflection, rotation, and translocation to put the zero in the top left square, with the smallest possible number beside it, the next smallest possible below it. 2 in the formula for U , the mathematical equivalent of normalising the duplicates and keeping the zero in the top left position. Reflections and Rotations. These rise from using all possible combinations of Graeco-Latin squares.