Nathan Chapelier‐Laget

activity

20202024

collaborators

5 papers

math.CO2024

A counterexample to a Brenti-Carnevale conjecture

Nathan Chapelier-Laget, Jean Fromentin

Recently, F. Brenti put a preprint on the arXiv with several interesting open problems on Coxeter groups and unimodality. In this note, we refute one of these conjectures with a co…

math.CO2021

Lattice associated to a Shi variety

Nathan Chapelier-Laget

Let $W$ be a irreducible Weyl group and $W_{a}$ its affine Weyl group. In a previous article the author defined an affine variety $X_{W_{a}}$ , called the Shi variety of $W_{a}$ …

math.CO2021

Affine twisted length function

Nathan Chapelier-Laget

Let $W_{a}$ be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements $w \in W_{a}$ in terms of $Φ^{+}$ -tuples $(k (w, α))_{α \in Φ^{+}}$ called the Shi vectors. Us…

math.CO2020

An order on circular permutations

Antoine Abram, Nathan Chapelier-Laget, Christophe Reutenauer

Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_{n}$ (that is, $n$ -cycles). It is isomorphic…

math.CO2020

Shi variety corresponding to an affine Weyl group

Nathan Chapelier-Laget

Let $W$ be an irreducible Weyl group and $W_{a}$ its affine Weyl group. In this article we show that there exists a bijection between $W_{a}$ and the integral points of an affine varie…