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    Latin Rectangle

    Definition

    A k×n Latin rectangle is a k×n matrix with elements a_(i j) element {1, 2, ..., n} such that entries in each row and column are distinct. If k = n, the special case of a Latin square results. A normalized Latin rectangle has first row {1, 2, ..., n} and first column {1, 2, ..., k}. Let L(k, n) be the number of normalized k×n Latin rectangles, then the total number of k×n Latin rectangles is N(k, n) = (n!(n - 1)!L(k, n))/((n - k)!) (McKay and Rogoyski 1995), where n! is a factorial. Kerewala found a recurrence relation for L(3, n), and Athreya et al. (1980) found a summation formula for L(4, n).

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