4 papers
Fixed points of DT transformations, cluster exponents and degrees of Weyl groups
Antoine de Saint Germain, Jiang-Hua Lu
Inspired by a recent work of Y. Mizuno, we show that the DT transformations on a cluster ensemble of finite type admit unique totally positive fixed points, and that the exponents…
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…
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…
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…