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Surface cluster algebra expansion formulae via loop graphs

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Wilson, Jonathan ORCID: 0000-0002-0840-5462 (2020) Surface cluster algebra expansion formulae via loop graphs. Journal of Combinatorial Theory Series A .

[thumbnail of surfaceclusteralgebraexpansions.pdf]

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Available under License Creative Commons Attribution.
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Official URL: https://arxiv.org/abs/2006.13218

Abstract

In 2011 Musiker, Schiffler and Williams obtained expansion formulae for cluster algebras from orientable surfaces. For singly and doubly notched arcs these formulae required the notion of γ-symmetric perfect matchings and γ-compatible pairs of γ-symmetric perfect matchings, respectively. We simplify and unify these approaches by considering good matchings of loop graphs.

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