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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)
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)
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)
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)
This article presents a methodology that automatically derives a combinato-rial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is achieved considering both pattern avoidance and pattern containment constraints in permutations. The obtained(More)