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math.RA — Rings and Algebras

Algebraic dependence of cluster X-variables

Contributed by 琪越唐

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.

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

Oct 05, 2026PDF ↗View work →

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Algebraic dependence of cluster X-variables

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