Using the double-cut-and-join (DCJ) model for genome rearrangement we use combinatorial techniques to analyze the distribution of genomes under DCJ distance. We present an exponential generating function for the number of genomes that are maximally distant from a given genome and provide a formula for the number of genomes that are any given distance from an arbitrary starting genome.
Jacqueline Christy. Joshua McHugh. Manda Riehl. Noah Williams. "Distribution of genome rearrangement distance under double cut and join." Involve 7 (4) 491 - 507, 2014. https://doi.org/10.2140/involve.2014.7.491