Parking functions, labeled trees and DCJ sorting scenarios

TL;DR

This paper provides an exact enumeration formula for DCJ rearrangement scenarios in genome rearrangement theory and establishes bijections with combinatorial objects like parking functions and labeled trees.

Contribution

It introduces a precise formula for counting DCJ scenarios and links them to well-known combinatorial structures, advancing understanding in genome rearrangement analysis.

Findings

Exact enumeration formula for DCJ scenarios

Bijections with parking functions and labeled trees

Enhanced tools for statistical analysis of genome rearrangements

Abstract

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.