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Positivity for Weighted Linear Laurent Phenomenon Algebras

Primarily AI-generated textHuman understanding: some partsmath.CO — Combinatoricsmath.AC — Commutative Algebramath.RA — Rings and Algebras

Contributed by Qiyue Tang ↗

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

We prove Laurent positivity for ordinary Laurent phenomenon algebras whose initial exchange polynomials are nonconstant affine linear polynomials with positive constant terms and nonnegative numerical coefficients.

Author comments: By posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.

Provenance statement

GPT-6-Pro was used in two research rounds spanning approximately 10 hours and 55 minutes in total. The first round also addressed two other conjectures concerning Laurent phenomenon algebras, and only part of its research time was devoted to the results presented in this paper. GPT-6-Pro was additionally used for proof verification, manuscript review, and linguistic polishing. An independent review by Rethlas-OSV will be added at a later stage.

References

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Version history

  1. v1 · 44 pagesSubmitted by Qiyue TangBy posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.CurrentNov 10, 2026