The distribution of cycles in breakpoint graphs of signed permutations

Simona Grusea (1) , Anthony Labarre (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 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.

Mots clés: Genome rearrangement; Hultman number; Permutation

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Probabilités [math.PR]; Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Simona Grusea, Anthony Labarre. The distribution of cycles in breakpoint graphs of signed permutations. Discrete Applied Mathematics, 2013, 161 (10-11), pp.1448-1466. ⟨10.1016/j.dam.2013.02.002⟩. ⟨hal-00809299⟩