Cluster algebras of type $\mathbb{A}_{n-1}$ through the permutation groups $S_{n}$
Kodjo Essonana Magnani
Volume 68, no. 1
(2025),
pp. 55–68
Published online (final version): February 28, 2025
https://doi.org/10.33044/revuma.3473
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Abstract
Flips of triangulations appear in the definition of cluster algebras by Fomin and
Zelevinsky. In this article we give an interpretation of mutation in the sense of
permutation using triangulations of a convex polygon. We thus establish a link between
cluster variables and permutation mutations in the case of cluster algebras of type
$\mathbb{A}$.
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