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Acyclic cluster algebras, reflection groups, and curves on a punctured disc.

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


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.

Item Type:Article
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Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:15 October 2018
Date deposited:16 October 2018
Date of first online publication:22 October 2018
Date first made open access:22 October 2019

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