559 citations · 1.2k across the 37 of their papers we have counts for
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math.RA2006★ 11 cited
Cluster algebras and triangulated surfaces. Part I: Cluster complexes
Sergey Fomin, Michael Shapiro, Dylan Thurston
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such…
math.RA2006★ 31 cited
Cluster algebras IV: Coefficients
Sergey Fomin, Andrei Zelevinsky
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initia…