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Surface cluster algebra expansion formulae via loop graphs

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Wilson, Jonathan orcid iconORCID: 0000-0002-0840-5462 (2026) Surface cluster algebra expansion formulae via loop graphs. Journal of Combinatorial Theory, Series A, 224 . p. 106224. ISSN 0097-3165

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Official URL: https://doi.org/10.1016/j.jcta.2026.106224

Abstract

In 2011 Musiker, Schiffler and Williams obtained expansion formulae for cluster algebras from orientable surfaces [16]. 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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