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Cluster scattering diagrams of acyclic affine type

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arxiv 2205.05125 v4 pith:IRN3FD2X submitted 2022-05-10 math.CO math.RT

Nathan Reading , Salvatore Stella This is my paper · ORCID
classification math.COmath.RT
keywords clusterscatteringacyclicaffinetypealmost-positivecoincidesconstructed
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We give an explicit construction of the cluster scattering diagram for any acyclic exchange matrix of affine type. We show that the corresponding cluster scattering fan coincides both with the mutation fan and with a fan constructed in the almost-positive roots model.

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Cited by 2 Pith papers

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  1. Dominance regions for affine cluster algebras

    math.RT 2025-12 conditional novelty 7.0 of 10

    In affine-type cluster algebras, dominance regions are points inside the g-vector fan and explicitly described line segments on the imaginary wall, with an integral version for lattice points.

  2. Local and global patterns of rank 3 $G$-fans of totally-infinite type

    math.CO 2024-11 conditional novelty 6.0 of 10

    Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.

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