Snake graph calculus and cluster algebras from surfaces (1209.4617v2)

Published 20 Sep 2012 in math.RT and math.CO

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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