Antoine de Saint Germain

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20232026

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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.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.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…