Parking functions, labeled trees and DCJ sorting scenarios

Details Parking functions, labeled trees and DCJ sorting scenarios Parking functions, labeled trees and DCJ sorting scenarios

2009-03-13

arxiv.org/abs/0903.2499v1

Computer Science

Discrete Mathematics

12 pages, 3 figures

Scientific paper

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.

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