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Superunitary regions of cluster algebras

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arxiv 2208.14521 v1 pith:G4YXWXYH submitted 2022-08-30 math.CO math.AC

Emily Gunawan , Greg Muller This is my paper · ORCID
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keywords clusterregionsuperunitaryalgebrapositiveadmitsalgebrasapplication
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This note introduces the superunitary region of a cluster algebra, the subspace of the totally positive region on which each cluster variable is at least 1. Our main result is that the superunitary region of a finite type cluster algebra is a regular CW complex which is homeomorphic to the generalized associahedron of the cluster algebra. As an application, the compactness of the superunitary region implies that each Dynkin diagram admits finitely many positive integral friezes.

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  1. 2-periodic frieze patterns

    math.RA 2025-06 conditional novelty 7.0 of 10

    Every 2-periodic positive real mesh frieze of finite type A, D or E is constant, or lies in a one- or two-parameter family, with the exact count depending on the type.

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