Scattering fan–mutation fan coincidence conjecture

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Let BB be an exchange matrix. The scattering fan–mutation fan coincidence conjecture. The scattering fan ScatFan⁡T ⁣(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.

References

Primary source

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

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