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Singleton Dominance Regions in Affine Cluster Algebras

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theorymath.CO — Combinatorics

Contributed by Qiyue Tang ↗

Version 1 / Nov 07, 2026 / CC BY 4.0

Abstract

For an extended exchange matrix of affine type, the dominance region of every point in an extended (g)-vector cone consists of that point alone.

Provenance statement

GPT-6-Pro was used in the research run that produced the proof. The full run lasted approximately two hours. Codex was used to review the proof and polish the exposition. A Rethlas-OSV review is planned for a later stage.

References

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  6. F. Qin, Bases for upper cluster algebras and tropical points , J. Eur. Math. Soc. 26 (2024), 1255--1312.
  7. N. Reading, D. Rupel, and S. Stella, Dominance regions for affine cluster algebras , arXiv:2512.02218v2 (https://arxiv.org/abs/2512.02218v2), 2026.arXiv
  8. N. Reading and D. E. Speyer, Cambrian frameworks for cluster algebras of affine type , Trans. Amer. Math. Soc. 370 (2018), 1429--1468.
  9. N. Reading and S. Stella, An affine almost positive roots model , J. Comb. Algebra 4 (2020), 1--59.
  10. N. Reading and S. Stella, Cluster scattering diagrams of acyclic affine type , arXiv:2205.05125v5 (https://arxiv.org/abs/2205.05125v5), 2026.arXiv
Show all 12 referencesShow fewer references
  1. N. Reading and S. Stella, Theta functions in acyclic affine type , arXiv:2603.23429v1 (https://arxiv.org/abs/2603.23429v1), 2026.arXiv
  2. D. Rupel and S. Stella, Dominance regions for rank two cluster algebras , Ann. Comb. 27 (2023), 873--894.

Version history

  1. v1 · 6 pagesSubmitted by Qiyue TangInitial depositCurrentNov 07, 2026