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Article Dans Une Revue Theoretical Computer Science Année : 2010

Posets and Permutations in the Duplication-Loss Model: Minimal Permutations with d Descents.

Résumé

In this paper, we are interested in the combinatorial analysis of the whole genome duplication - random loss model of genome rearrangement initiated in a paper of Chaudhuri, Chen, Mihaescu, and Rao in SODA 2006 and continued by Bouvel and Rossin in 2007. In this model, genomes composed of n genes are modeled by permutations of the set of integers [1..n], that can evolve through duplication-loss steps. It was previously shown that the class of permutations obtained in this model after a given number p of steps is a class of pattern-avoiding permutations of finite basis. The excluded patterns were described as the minimal permutations with d=2^p descents, minimal being intended in the sense of the pattern-involvement relation on permutations. Here, we give a local and simpler characterization of the set B_d of minimal permutations with d descents. We also provide a more detailed analysis - characterization, bijection and enumeration - of two particular subsets of B_d, namely the patterns in B_d of size d+2 and 2d.
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Dates et versions

hal-00286561 , version 1 (09-06-2008)

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Mathilde Bouvel, Elisa Pergola. Posets and Permutations in the Duplication-Loss Model: Minimal Permutations with d Descents.. Theoretical Computer Science, 2010, 411 (26-28), pp.2487-2501. ⟨hal-00286561⟩
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