How many latin rectangles are there?

A de Gennaro�- arXiv preprint arXiv:0711.0527, 2007 - arxiv.org
A de Gennaro
arXiv preprint arXiv:0711.0527, 2007arxiv.org
Until now the problem counting Latin rectangles mxn 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.
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.
arxiv.org