Suppose (S, ∗) is a mathematical structure on a set S. As examples, (S, ∗) might be a topological space on S, a topological group on S, an n-ary operator on S, an n-ary relation on S or a Steiner triple system on S. A similarity mapping on (S, ∗) is a permutation on S that preserves the structure of (S, ∗). Such mappings f : (S, ∗) → (S, ∗) are called by different names. As examples, f might be...