nLab
Latin square

An n×nn \times n Latin square is a square array of numbers from 11 to nn such that each row and each column contains every number from 11 to nn. For example, an ordinary sudoku square is a special type of 9×99 \times 9 Latin square.

Latin squares can be regarded as precisely the multiplication tables for quasigroup structures on the set {1,2,,n}\{1, 2, \ldots, n\}, where iji j is the entry in the i thi^{th} row and j thj^{th} column. Indeed, the condition that no two entries in the i thi^{th} row are the same says that left multiplication by ii is invertible, and that no two entries in the j thj^{th} column are the same says that right multiplication by jj is invertible.

category: combinatorics

Last revised on August 26, 2018 at 08:20:07. See the history of this page for a list of all contributions to it.