High Quality Content by WIKIPEDIA articles! In the combinatorics and statistics, a Latin square is an n x n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column. In the design of experiments, Latin squares are a special case of row-column designs for two blocking factors: Many row-column designs are constructed by concatenating Latin squares. In algebra, Latin squares are generalizations of groups; in fact, Latin squares are characterized as being the multiplication tables of quasigroups. Other applications include error correcting codes. The name Latin square originates from Leonhard Euler, who used Latin characters as symbols. A Latin square is said to be reduced if its first row and first column are in natural order. For example, the Latin square above is reduced because both its first row and its first column are 1,2,3. We can make any Latin square reduced by permuting the rows and columns.

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