Latin rectangle

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In combinatorial mathematics, a Latin rectangle is an r × n matrix that has the numbers 1, 2, 3, ..., n as its entries with no number occurring more than once in any row or column where r ≤ n. An n × n Latin rectangle is called a Latin square. If r < n, then it is possible to append n − r rows to an r × n Latin rectangle to form a Latin square, using Hall's marriage theorem.

In statistics, Latin rectangles have applications in the design of experiments.

See also[edit]


  • Mirsky, L. Transversal Theory, New York, Academic Press, 1971.