Mappings of Latin squares (Q1362666)

Let \(L_n\) denote the set of \(n\) by \(n\) Latin squares. A set of mappings connects \(L_n\) if for any two Latin squares \(A\) and \(B\) there is a mapping of this set that maps \(A\) to \(B\). The author defines two classes of ``symbol operations'' (Definitions 2.2 and 2.3) whose union connects \(L_n\). This set has the smallest cardinality among the known sets of mappings that connect \(L_n\). As an application, is it shown how the symbol operations can be used for generating a uniform distribution on \(L_n\) by a Markov chain.