The distribution of cycles in breakpoint graphs of signed permutationsReport as inadecuate

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* Corresponding author 1 ESP - Equipe de Statistique et Probabilités ESP - IMT IMT - Institut de Mathématiques de Toulouse UMR5219, Institut de Mathématiques de Toulouse 2 LIGM - Laboratoire d-Informatique Gaspard-Monge

Abstract : Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of dissimilarity between genomes, and studying the distribution of those cycles is therefore critical to gaining insight on the distributions of the genomic distances that rely on it. We extend here the work initiated by Doignon and Labarre 6, who enumerated unsigned permutations whose breakpoint graph contains k cycles, to signed permutations, and prove explicit formulae for computing the expected value and the variance of the corresponding distributions, both in the unsigned case and in the signed case. We also show how our results can be used to derive simpler proofs of other previously known results.

keyword : Genome rearrangement Hultman number Permutation

Author: Simona Grusea - Anthony Labarre -



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