Block gluing in Hom shifts and path reconfiguration in graphs
summary: We study some tilings spaces that are defined from graph homomorphisms, called Hom shifts. Compared to general tiling spaces, they look the same in every direction (invariance by rotation and symmetry) and many undecidable problems or questions in tiling spaces seem to become easier for these objects, using graph-theoretical ...
Acyclic colorings of graphs and the probabilistic method
summary: Graph colorings have been extensively studied for the past century, due to the richness of the theory and its numerous applications. Part of the current research focuses on constrained colorings, and how their properties differ from proper colorings. When we require that, in a proper coloring, no (even) cycle ...
From Delta to Theta conjectures: a survey
In 2015, Haglund Remmel and Wilson proposed two conjectural combinatorial interpretations of a certain symmetric function involving a certain Delta operator, which acts diagonally on the MacDonald polynomials. These formulas generalise the shuffle conjecture (Haglund, Haimal, Loehr, Remmel, Ulyanov 2002), now theorem (Carlsson, Mellit 2018). In this talk, we will ...
Tiling Groups: Emptiness and Aperiodicity
summary: Tilings of the plane or infinite grid have been a rich field of study for many years. Through tiling with local rules, it is even possible to create aperiodicity and embed computation in the plane. But what happens when we begin changing the underlying structure? We will explore how ...
Vingt mille lieues sous les mots
summary: Dans cette présentation, nous découvrirons une partie de l'écosystème de l'océan de la combinatoire de mots, dont l'exploration a commencé depuis plus d'un siècle. À la surface vivent d'abord les mots périodiques, aux propriétés très régulières et simples : ils nous serviront de point d ...
Introduction à l'apprentissage par renforcement
summary: Cet exposé proposera une introduction à l'apprentissage par renfocement, en présentant les fonctions à maximiser et les types d'approches employées. La présentation suivra l'évolution historique du domaine, du Q-Learning au Deep Reinforcement Learning, en passant par des travaux étant devenus populaires tel que AlphaGo. Nous conclurons ...
Strong local rules without labels for Penrose rhombus tilings
summary: The Penrose rhombus tilings are a subshift of tilings of the planefirst defined by R. Penrose. This subshift is crucial in the study of geometrical tilings because, though it was originally defined with 2 rhombus tiles with cuts-and-notches or arrows on the edges, it is an aperiodic subshift with ...
Multitriangulations and tropical Pfaffians
The \(k\)-associahedron \(Ass_k(n)\) is the simplicial complex of \((k+1)\)-crossing-free subgraphs of the complete graph with vertices on a circle. Its facets are called \(k\)-triangulations. We explore the connection of \(Ass_k(n)\) with the Pfaffian variety \(Pf_k(n)\subset K^\binom{n}{2}\) of antisymmetric matrices ...
Efficient generation of rectangulations and elimination trees via permutation languages
In this talk we apply the Hartung-Hoang-Mütze-Williams permutation language framework to derive exhaustive generation algorithms for two further classes of combinatorial objects, as well as Hamilton paths and cycles on the corresponding polytopes: (3) different classes of rectangulations, which are subdivisions of a rectangle into smaller rectangles (see www.combos ...
Combinatorial generation via permutation languages
In this talk we present a versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This framework provides a unified view on many known Gray code results and allows us to prove many new ones, and it yields efficient algorithms ...