2 problems

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Connectedness conjecture for the mutation graph of cotorsion pairs
Let $\mathcal{C}$ be an indecomposable $2$ -Calabi–Yau triangulated category, and let $\mathscr{M}(\mathcal{C})$ be the quiver whose vertices are cotorsion pairs in $\mathcal{C}$ , w…
Conjectureopen2-calabi-yau-categories cluster-mutation cotorsion-pairsarXiv posted 2 days ago
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Mutation invariance of generic cluster characters
Mutation-invariance conjecture. Under these assumptions, the diagram identifying cluster monomials with generic characters via $\phi$ commutes:
Conjectureopencategorification cluster-algebras cluster-mutationarXiv posted 2 days ago

Connectedness conjecture for the mutation graph of cotorsion pairs