Latin square

Summary

A Latin square of order $n$ is an $n \times n$ array filled with $n$ symbols. Each symbol occurs exactly once in each row and exactly once in each column. Latin squares are the multiplication tables of quasigroups, and the Cayley tables of finite groups are examples. They are used in the design of experiments and in coding theory, and orthogonal families of them are tied to finite projective planes. The node Latin square gives the precise definition.