Article ID Journal Published Year Pages File Type
419675 Discrete Applied Mathematics 2013 19 Pages PDF
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 (dis)similarity 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 kk 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.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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