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On the approximate periodicity of sequences attached to non-crystallographic root systems. (English) Zbl 1423.13126
Summary: We study Fomin-Zelevinsky’s mutation rule in the context of non-crystallographic root systems. In particular, we construct approximately periodic sequences of real numbers for the non-crystallographic root systems of rank 2 by adjusting the exchange relation for cluster algebras. Moreover, we describe matrix mutation classes for types \(H_3\) and \(H_4\).

13F60 Cluster algebras
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