Encyclopedia of Social Science Research Methods

Latin Square

A Latin square is a square array of letters or ordered symbols in which each letter or symbol appears once and only once in each row and each column. The following are examples of 2 × 2, 3 × 3, and 4 × 4 Latin squares.

The name Latin square was given to the squares by the famous Swiss mathematician Leonard Euler (1707-1783), who studied them and used letters of the Latin alphabet.

The three squares in the table above are called standard squares because their first row and first column are ordered alphabetically. Two Latin squares are conjugate if the rows of one square are identical to the columns of the other. For example, a 5×5 Latin square and its conjugate are as follows:

A Latin square is self-conjugate if the same square is obtained when its rows and columns are interchanged. The 2 ...

—Roger E. Kirk