Parking Functions, Labeled Trees and DCJ Sorting Scenarios

Authors:
Aïda Ouangraoua;Anne Bergeron
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, Canada and Lacim, Université du Québec à Montréal, Montréal, Canada;Lacim, Université du Québec à Montréal, Montréal, Canada
Venue:
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
Year:
2009

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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.