On the number of Latin squares

We ( 1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, ( 2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f ! where f is a particular integer close to 1/2 n, ( 3) provide a formula for the number of Latin squares in terms of permanents of (+ 1; 1)- matrices, ( 4) find the extremal values for the number of 1-factorisations of k-regular bipartite graphs on 2n vertices whenever 1 <= k <= n <= 11, ( 5) show that the proportion of Latin squares with a non-trivial symmetry group tends quickly to zero as the order increases.