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Cluster-cyclic condition of skew-symmetrizable matrices of rank 3 via the Markov constant

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arxiv 2411.07083 v2 pith:U5MDUUF2 submitted 2024-11-11 math.CO math.AG

Ryota Akagi This is my paper · ORCID
classification math.COmath.AG
keywords matricesskew-symmetrizableconstantmarkovmutationsquiverrankalready
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In this paper, we consider mutations of skew-symmetrizable matrices of rank 3. Every skew-symmetrizable matrix corresponds to a weighted quiver, and we study the conditions when this quiver is always cyclic after applying mutations. In this study, the Markov constant has an essential meaning. It has already appeared in some previous works for skew-symmetric matrices.

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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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