Bangle functions are the generic basis for cluster algebras from punctured surfaces with boundary

Christof Geiß, Daniel Labardini-Fragoso, Jon Wilson

We prove that for any possibly-punctured surface with non-empty boundary $\hat{\mathbf{I}}\pounds =(\hat{I}\pounds ,\mathbb{M},\mathbb{P})$, and any tagged triangulation $T$ of $\hat{\mathbf{I}}\pounds$ in the sense of F…