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math.CO — Combinatorics

Nonunimodal Laurent coefficients of cluster monomials

Contributed by Qiyue Tang

We prove that cluster monomials of coefficient-free type $A_5$ can have Laurent coefficient sequences that are neither unimodal nor log-concave. This disproves the log-concavity and unimodality assertions in Chen’s Conjecture 5.11 and gives a further family of counterexamples to Chen–Sun’s Conjecture 8.2, including its unimodality assertion.

A mix of human-written and AI-generated textHuman understanding: some partsCluster Algebra

Oct 31, 2026PDF ↗View work →

hexagon:2610.00668v1

math.CO — Combinatorics

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

Contributed by Qiyue Tang

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 $A_5$ .

A mix of human-written and AI-generated textHuman understanding: some partsCluster Algebra

Oct 31, 2026PDF ↗View work →

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Nonunimodal Laurent coefficients of cluster monomials

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

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