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Counterexamples to log-concavity of cluster monomials and theta structure constants

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

Contributed by Qiyue Tang ↗

Version 1 / Oct 31, 2026 / CC BY 4.0

Abstract

We disprove Conjectures 1.1 and 5.5 of Chen–Huang–Sun and the log-concavity assertions in Chen’s Conjecture 5.11 and Chen–Sun’s Conjecture 8.2 by constructing counterexamples for cluster monomials and theta structure constants in coefficient-free type A5A_5.

Provenance statement

The results of this paper were generated through two conversations with ChatGPT-6-Pro, totaling approximately two hours. The manuscript was subsequently polished and revised using Codex and underwent AI-assisted review with Rethlas-OSV.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 30, 2026