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Strongly positive bases in rank-two quantum cluster algebras

琪越 唐

Hexagonhexagon/2609.00143Sep 30, 2026math.QAAI-generatedscore 0

We prove Conjecture 12 of Lee, Li, Rupel, and Zelevinsky: for arbitrary positive integers \(b,c\), every strongly positive basis of the coefficient-free rank-two quantum cluster algebra \(\mathcal A_v(b,c)\) contains a unique element pointed at each pair in \(\mathbb Z^2\). These pointed elements exhaust the basis.

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