Publication details for Pavel TumarkinFelikson, A. & Tumarkin, P. (2018). Acyclic cluster algebras, reflection groups, and curves on a punctured disc. Advances in Mathematics 340: 855-882.
- Publication type: Journal Article
- ISSN/ISBN: 0001-8708
- DOI: 10.1016/j.aim.2018.10.020
- Further publication details on publisher web site
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Author(s) from Durham
We establish a bijective correspondence between certain non-self-intersecting curves in an n-punctured disc and positive c-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corollary, we obtain a proof of Lee–Lee conjecture  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.