  In the context of the genome rearrangement problem, we analyze two well known
models, namely the block transposition and the prefix block transposition
models, by exploiting the connection with the notion of permutation pattern.
More specifically, for any $k$, we provide a characterization of the set of
permutations having distance $\leq k$ from the identity (which is known to be a
permutation class) in terms of what we call generating permutations and we
describe some properties of its basis, which allow to compute such a basis for
small values of $k$.
