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A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden permutations, are partially well ordered, and have(More)
LIAFA Motivations and the model Previous results Combinatorial properties Other questions Outline of the talk 1 Biological motivations and the combinatorial model 2 Previous results: the whole genome duplication-random loss model 3 Some combinatorial properties of the classes C(K , 1) and C(K , p) 4 Other questions to be considered Mathilde Bouvel A variant(More)
In this paper, we are interested in the combinatorial analysis of the whole genome duplication-random loss model of genome rearrangement initiated in [8] and [7]. In this model, genomes composed of n genes are modelled by permutations of the set of integers [1..n], that can evolve through duplication-loss steps. It was previously shown that the class of(More)
A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show that, despite this worst-case analysis, with probability one, sorting can be done in polynomial time. Further, we find(More)