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A Finite Polyhedral Construction of the Rank-Two Quantum Greedy Basis

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.CO — Combinatoricsmath.RA — Rings and Algebras

Contributed by 琪越 唐 ↗

Version 1 / Oct 03, 2026 / CC BY 4.0

Abstract

We give a finite polyhedral construction of the quantum greedy basis for coefficient-free rank-two quantum cluster algebras. The construction specializes coefficientwise to the classical polyhedral construction at v = 1. Corresponding classical and quantum coefficients and auxiliary margins have identical zero sets, and the Newton polytopes are affine images of the classical carriers.

Provenance statement

The idea came from the author, with reference to the work of Fang Li and Jie Pan. In the process of developing the specific analogy, the author conversed extensively with GPT-6-Astra and used Danus to tackle some of the more difficult theorems.

References

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  3. Lee, Kyungyong; Li, Li; Rupel, Dylan; Zelevinsky, Andrei. The existence of greedy bases in rank 2 quantum cluster algebras. Advances in Mathematics, vol. 300, pp. 360–389. 2016. Preprint version used for numbered references: arXiv:1405.2414v1arXivDOI
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Version history

  1. v1Initial depositCurrentOct 03, 2026Submitted by 琪越 唐