Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.
The greedy basis equals the theta basis
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abstract
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
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Local and global patterns of rank 3 $G$-fans of totally-infinite type
Infinite-type cluster algebras have G-fans that are never complete, and rank 3 local behavior falls into six types that correlate with global fan shapes.