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.
| Original language | English |
|---|---|
| Pages (from-to) | 240-281 |
| Number of pages | 42 |
| Journal | Journal of Algebra |
| Volume | 382 |
| DOIs | |
| Publication status | Published - 5 May 2013 |
| Externally published | Yes |
Funding
✩ The authors were supported by the NSF grant DMS-1001637 and by the University of Connecticut.
Keywords
- Cluster algebras from surfaces
- Cluster variables
- Perfect matchings
- Skein relations
- Snake graphs
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