**Organisateurs :** D. Bertrand, B. Chauvin, L. Di Vizio

**Programme de la journée : **

10h30 : accueil des participants, café

11h-12h : M. Wibmer (RWTH Aachen), Skolem-Mahler-Lech type theorems and Picard-Vessiot theory

Résumé : After recalling some basics of the Galois theory of linear difference equations, I will explain how this theory can be applied to study holonomic sequences. In particular, I will point out a connection between this Galois theory and a generalization of the Skolem-Mahler-Lech theorem to rational function coefficients.

14h-15h : A. Bostan (SpecFun, INRIA Saclay), Computer Algebra for Lattice Path Combinatorics

Résumé : Classifying lattice walks in restricted lattices is an important problem in enumerative combinatorics. Recently, computer algebra methods have been used to explore and solve a number of difficult questions related to lattice walks. In this talk, we will give an overview of recent results on structural properties and explicit formulas for generating functions of walks in the quarter plane, with an emphasis on the algorithmic methodology.

15h30-16h30 : M. Bousquet-Mélou (CNRS et Université Bordeaux 1), Permutations sortable by two parallel stacks and quarter plane walks.

Résumé : The problem of enumerating the permutations that can be sorted using two stacks in parallel has stood open since it was raised in the early 1970s. We solve it by giving a pair of functional equations that characterizes the generating function of permutations that can be sorted with two parallel stacks. The first component of this system describes the generating function Q(a,u) of square lattice loops confined to the positive quadrant, counted by the length and the number of northeast corners. Our analysis of the asymptotic number of sortable permutations relies at the moment on two intriguing conjectures dealing with the series Q(a,u). We prove that these conjectures hold for closed walks confined to the upper half-plane, or not confined at all. They remain open for quarter plane walks. Given the recent activity on walks confined to cones, we believe them to be attractive per se.

**La journée aura lieu le matin au bâtiment Buffon, amphi Bertin, et l’après-midi au bâtiment Fermat, amphi H. Confirmez votre participation au déjeuner en envoyant un mail à divizio[at]math.cnrs.fr **