Mappings of latin squares

Let Ln denote the set of n by n Latin squares. We show that it is possible to map from one such square A to another square B using only the class of mappings defined by (1) symbol interchanges on cycles defined by two symbols and (2) a restricted class of mappings involving three symbols. The total number of mappings so defined is the smallest known class sufficient to connect Ln. As an application of this result, we define a Markov chain on Ln whose asymptotic distribution is uniform, thus providing a means of generating uniformly distributed Latin squares.