Open Research Index

Algebraic dependence of cluster X-variables

琪越 唐

Hexagonhexagon/2610.00031Oct 5, 2026math.RAAI-generatedscore 0

We prove that, over any field and with algebraically independent initial seed coordinates, two cluster \(X\)-variables are algebraically dependent if and only if they are equal or reciprocal. In characteristic zero, this is equivalent to the vanishing of the wedge product of their differentials.

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