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Latin rectangle information


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
  1. ^ Colbourn & Dinitz 2007, p. 141.
  2. ^ Stones 2010.
  3. ^ Brualdi 2010, p. 385

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