Snake graph calculus and cluster algebras from surfaces II: Self-crossing snake graphs

Understand

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 continue our study of snake graphs from a combinatorial point of view.
• We introduce the notions of abstract snake graphs and abstract band graphs, their crossings and self-crossings, as well as the resolutions of these crossings.