# Latin squares of order 11

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 n/2, (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.
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