Title: Acyclic cluster algebras, reflection groups, and curves on a punctured disc,
Abstract: We establish a bijective correspondence between certain non-self-intersecting
curves in an $n$-punctured disc and positive ${\mathbf c}$-vectors of acyclic
cluster algebras whose quivers have multiple arrows between every pair of
vertices. As a corollary, we obtain a proof of a conjecture by K.-H. Lee and K.
Lee (arXiv:1703.09113) on the combinatorial description of real Schur roots for
acyclic quivers with multiple arrows, and give a combinatorial characterization
of seeds in terms of curves in an $n$-punctured disc.