Antoine de Saint Germain

collaborators

6 papers

math.CO2024

On upper bounds of frieze patterns

Jon Cheah, Antoine de Saint Germain

In this note, we show that the sequence of maximum values in frieze patterns of type $A_{n}$ is the sequence of Fibonacci numbers, and that of frieze patterns of type $C_{n}$ is the se…

math.RT2024

Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel

Peigen Cao, Antoine de Saint Germain, Jiang-Hua Lu

We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In…

math.CO2024

When frieze patterns meet Y-systems: Y-frieze patterns

Antoine de Saint Germain

We give an elementary account of the notion of Y-frieze patterns, explain some of their properties, and reveal their connection with Coxeter's frieze patterns.

math.RA2023

Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel

Peigen Cao, Antoine de Saint Germain, Jiang-Hua Lu

We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In…

math.CO2023

Y-frieze patterns

Antoine de Saint Germain

Motivated by cluster ensembles, we introduce a new variant of frieze patterns associated to acyclic cluster algebras, which we call $Y -frieze patterns$ . Using the mu…

math.RA2023

Friezes of cluster algebras of geometric type

Antoine de Saint Germain, Min Huang, Jiang-Hua Lu

For a cluster algebra $A$ over $Q$ of geometric type, a $frieze$ of $A$ is defined to be a $Q$ -algebra homomorphism from $\mathcal{A}…