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The greedy basis equals the theta basis

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arxiv 1508.01404 v2 pith:3CQSL4SL submitted 2015-08-06 math.QA math.AGmath.CO

Man Wai Cheung , Mark Gross , Greg Muller , Gregg Musiker , Dylan Rupel , Salvatore Stella , Harold Williams This is my paper · ORCID
classification math.QAmath.AGmath.CO
keywords basisgreedythetaalgebrabasescanonicalclusterequality
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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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  1. Local and global patterns of rank 3 $G$-fans of totally-infinite type

    math.CO 2024-11 conditional novelty 6.0 of 10

    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.

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