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

Parking functions, labeled trees and DCJ sorting scenarios