Scattering fan–mutation fan coincidence conjecture

Let BB be an exchange matrix. The scattering fan–mutation fan coincidence conjecture. The scattering fan ScatFanT ⁣(B)\operatorname{ScatFan}^T\!(B) coincides with the mutation fan FBT\mathcal F_{B^T} if and only if either

  1. BB is 2×22\times 2 and of finite or affine type; or
  2. BB is n×nn\times n for n>2n>2 and of finite mutation type.

The conjecture characterizes exactly when the scattering fan and mutation fan agree; in general, the scattering fan is known to refine the mutation fan, while the asserted converse classification is not resolved in the supplied source.

Sources & referencesView supporting material

Primary source

Nathan Reading and Salvatore Stella, “Cluster scattering diagrams of acyclic affine type”, arXiv:2205.05125 (2025).

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