
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 ...