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Durham University

Department of Mathematical Sciences


Publication details for Pavel Tumarkin

Felikson, A. & Tumarkin, P. (2018). Acyclic cluster algebras, reflection groups, and curves on a punctured disc. Advances in Mathematics 340: 855-882.

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 [15] 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.