Felikson, A. and Tumarkin, P. (2018) 'Acyclic cluster algebras, reflection groups, and curves on a punctured disc.', Advances in mathematics., 340 . pp. 855-882.
Abstract
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 |
|---|---|
| Full text: | (AM) Accepted Manuscript Download PDF (472Kb) |
| Status: | Peer-reviewed |
| 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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