Combinatorics of Permutations, 2nd Edition

9

How Did We Get Here? Permutations as

Genome Rearrangements.

9.1 Introduction

Let p and q be two permutations, written in one-line notation. In this section,

we will attempt to transform p into q using only certain kinds of allowed steps.

If k is the smallest integer so that p can be transformed into q using k legal

steps, then we say that the distance d(p, q)ofp and q is k.

The motivation for this research comes from molecular biology, where genomes

of various species can be modeled by permutations, and the distance between

these permutations can be interpreted as the evolutionary distance between

species. A classic paper of the field, [167] by Shridhar ...