Permutation patterns in genome rearrangement problems: the reversal model

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