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  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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1016/j.aim.2018.10.020|
|Publisher statement:||© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/|
|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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