In combinatorial mathematics, a Latin rectangle is an r × n matrix (where r ≤ n), using n symbols, usually the numbers 1, 2, 3, ..., n or 0, 1, ..., n − 1 as its entries, with no number occurring more than once in any row or column.[1]
An n × n Latin rectangle is called a Latin square. Latin rectangles and Latin squares may also be described as the optimal colorings of rook's graphs, or as optimal edge colorings of complete bipartite graphs.[2]
An example of a 3 × 5 Latin rectangle is:[3]
| 0 | 1 | 2 | 3 | 4 |
| 3 | 4 | 0 | 1 | 2 |
| 4 | 0 | 3 | 2 | 1 |