# Permutation patterns in genome rearrangement problems: the reversal model

## TL;DR

This paper explores the relationship between permutation patterns and genome rearrangement models, specifically reversal and prefix reversal, providing characterizations and basis computations for permutations close to the identity.

## Contribution

It introduces a novel characterization of permutations within a certain distance from the identity using generating peg permutations in the context of genome rearrangement models.

## Key findings

- Characterization of permutations with distance ≤ k from the identity
- Description of properties of the basis of permutation classes
- Method to compute the basis for small values of k

## Abstract

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 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 peg permutations and we describe some properties of its basis, which allow to compute such a basis for small values of $k$.