Snake graph calculus and cluster algebras from surfaces
Representation Theory
2012-10-22 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1209.4617,
title = {Snake graph calculus and cluster algebras from surfaces},
author = {Ilke Canakci and Ralf Schiffler},
journal= {arXiv preprint arXiv:1209.4617},
year = {2012}
}
Comments
37 pages, 29 Figures; v2 Theorem 5.4 added