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arXiv · 1209.4617

Snake graph calculus and cluster algebras from surfaces

Ilke Canakci·Ralf Schiffler
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Abstract

Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we identify each cluster variable with its snake graph, and interpret relations among the cluster variables in terms of these graphs. In particular, we give a new proof of skein relations of two cluster variables.

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Ilke Canakci, Ralf Schiffler. 2012-09-20. Snake graph calculus and cluster algebras from surfaces. https://arxiv.org/abs/1209.4617

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