The fixed-point construction in tilings
summary: Consider a tileset, i.e. a finite set of colors along with some adjacency constraints between them. It defines the set of colorings of the infinite grid that respects these adjacency constraints. Such a coloring is called a tiling. Given a tileset as input, a question naturally arises: does ...
Lattice properties of acyclic pipe dreams
summary: Pipe dreams were introduced by Bergeron and Billey in order to study Schubert polynomials and encode the algebraic structure of the symmetric group. In particular, with well-chosen parameters, they have the combinatorial structure of the Tamari lattice, a well-known quotient of the weak order on permutations. In this presentation ...
Séries génératrices et preuves d'intrinsèque ambiguïté
Cet exposé porte sur la connexion entre l'intrinsèque ambiguïté en théorie des langages formels, et les propriétés des séries génératrices des langages associés. Il est bien connu que les langages réguliers ont des séries génératrices rationnelles et que les séries génératrices des langages algébriques non ambigus sont algébriques. Dans ...
Proper vertex coloring with odd occurrence - Probabilistic approach
summary: In graph theory, a graph coloring is an assignment of colors to elements of a graph subject to certain constraints. A vertex coloring is said to be proper if any pair of two adjacent vertices are assigned distinct colors. For a graph G, the chromatic number χ(G) is ...
Some results on directed coloring
summary: Proper coloring of undirected graphs lies among the most studied
problems in graph theory. It asks to color vertices while giving
different colors to adjacent ones.
In 1982, Neumann-Lara introduced a generalization of this problem to
directed graphs. When walking in an undirected graph, an undirected edge
between two ...
Associaèdres cycliques et degrés intrinsèques des arborescences non-croisées
Le polytope de pivot d'un polytope P est une généralisation de son polytope des chemins monotones qui vise a capturer le comportement de la "shadow vertex rule" (une règle de pivot importante en optimisation linéaire et dans le domaine des polytopes de fibre). Il a récemment été montré que ...
Walking On A Line: finding S-adic walks in an ω-automaton
summary: At the heart of symbolic dynamics lies the study of languages, infinite words and the dynamical structures associated. We focus on two classical methods to generate such structures. The first one relies on substitutions, which are morphisms on words, by iterating one on an initial letter, and considering the ...
Séminaire ouvert
Lors d'un séminaire ouvert, le thème n'est pas décidé à l'avance. Tous les membres du séminaires sont invités à participer et peuvent proposer le jour même des interventions plus ou moins longues, des démos ou des questions ouvertes au reste de l'équipe.
Realizing Geometrically s-Permutahedra via Flow Polytopes
summary: In 2020, Ceballos and Pons defined s-decreasing trees with s being a weak composition. They described an order on these objects called the s-weak order which gives them the order structure of a lattice. They further conjectured that this structure could be realized geometrically as the 1-skeleton of a ...
Density of sphere packings: from coins to oranges
summary: How to stack an infinite number of oranges to maximize the proportion of the covered space? Kepler conjectured that the "cannonball" packing is an optimal way to do it. This conjecture took almost 400 years to prove and the proof of Hales and Ferguson consists of 6 papers and ...