How many latin rectangles are there?

Details How many latin rectangles are there? How many latin rectangles are there?

2007-11-04

arxiv.org/abs/0711.0527v1

Mathematics

Combinatorics

Scientific paper

Until now the problem counting Latin rectangles m x n has been solved with an explicit formula for m = 2, 3 and 4 only. In the present paper an explicit formula is provided for the calculation of the number of Latin rectangles for any order m. The results attained up to now become particular cases of this new formula. Furthermore, putting m = n, the number of Latin squares of order n can also be obtained in an explicit form.

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