3 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 is the sequence of Fibonacci numbers, and that of frieze patterns of type 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.