In type A, two seeds determine the same point over F2 exactly when their triangulations are connected by hexagonal moves, and minimal seed sets can cover cluster manifolds over any field, although F2-only coverings also exist.
Cluster structures on braid varieties
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Cluster tori over $\mathbb{F}_2$, hexagonal moves on triangulations, and minimal coverings of cluster manifolds
In type A, two seeds determine the same point over F2 exactly when their triangulations are connected by hexagonal moves, and minimal seed sets can cover cluster manifolds over any field, although F2-only coverings also exist.