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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)
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)
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)
In this paper, we study the class of pin-permutations, that is to say of permutations having a pin representation. This class has been recently introduced in [16], where it is used to find properties (algebraicity of the generating function, decidability of membership) of classes of permutations, depending on the simple permutations this class contains. We(More)
In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall, Ruškuc, Vatter, Simple permutations: decidability and unavoidable substructures, 2008], and shares several aspects with(More)
Deciding the finiteness of the number of simple permutations contained in a wreath-closed class is polynomial *. Abstract We present an algorithm running in time O(n log n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of(More)
We suggest an approach for the enumeration of minimal permutations having d descents which uses skew Young tableaux. We succeed in finding a general expression for the number of such permutations in terms of (several) sums of determinants. We then generalize the class of skew Young tableaux under consideration; this allows in particular to recover a formula(More)
We study sorting operators A on permutations that are obtained composing Knuth's stack sorting operator S and the reversal operator R, as many times as desired. For any such operator A, we provide a size-preserving bijection between the set of permutations sorted by S • A and the set of those sorted by S • R • A, proving that these sets are enumerated by(More)