Tag: Combi seminar
Three interacting families of Fuss-Catalan posets
We will introduce three families of posets depending on a nonnegative integer parameter \(m\), having underlying sets enumerated by the \(m\)-Fuss Catalan numbers. Among these, one is a generalization of Stanley lattices and another one is a generalization of Tamari lattices. We will see how these three families of ...
Formes limites de permutations à motifs interdits
On s'intéresse aux ensembles de permutations à motifs exclus, appelés classes de permutations, qui ont été beaucoup étudiés en combinatoire énumérative. Dans ce travail, à la frontière entre combinatoire et probabilités, on s'intéresse à la limite d'échelle d'une grande permutation aléatoire uniforme dans une classe de ...
Cardinal d'un ensemble de coupure minimal en percolation de premier passage
On considère le modèle de percolation de premier passage sur \(\mathbb{Z}^d\) en dimension \(d\geq 2\) : on associe aux arêtes du graphe une famille de variables i.i.d. positives ou nulles. On interprète la variable aléatoire associée à une arête comme étant sa capacité, i.e., la ...
Permutahedral matchings, zonotopal tilings, and d-partitions
In this talk I will present higher dimensional generalizations of the following three concepts:
- (a) perfect matchings of a hexagonal tiling,
- (b) rhombus tilings of a hexagon, and
- (c) plane partitions.
I will show that these generalizations are equivalent under certain specific bijections. The generalizations of (b) and (c) have ...
Brauer-Thrall Conjectures, Old and New!
\(\tau\)-tilting theory is an elegant-- but technical-- subject in representation theory of associative algebras, with motivations from cluster algebras. It was introduced by Adachi-Iyama-Reiten, in 2014. However, thanks to the recent result of Demonet-Iyama-Jasso, one can fully phrase the concept of \(\tau\)-tilting finiteness in terms of linear algebra ...
Geometry of random permutation factorizations
We study random minimal factorizations of the \(n\)-cycle into transpositions, that is, factorizations of the cycle \((1 2...n)\) into a product of \(n-1\) transpositions. It is known that these factorizations are in bijection with Cayley trees of size \(n\), and therefore that there are \(n^{n-2}\) of them ...
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.
Bounded P-partition and Flagged P-partition
Travaux en commun avec Sami Assaf.
Improved bounds for centered colorings
A vertex coloring \phi of G is p-centered for each connected subgraph H of G either \phi uses more than p colors on H or or there is a color that appears exactly once on H. Centered colorings form one of the families of parameters that allow to capture notions ...
Independence Posets
Let G be an acylic directed graph. For each vertex of G, we define an involution on the independent sets of G. We call these involutions flips, and use them to define a new partial order on independent sets of G.
Trim lattices generalize distributive lattices by removing the graded ...