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Structure of seeds in generalized cluster algebras. (English) Zbl 1366.13017
Summary: We study generalized cluster algebras, introduced by L. Chekhov and M. Shapiro [Int. Math. Res. Not. 2014, No. 10, 2746–2772 (2014; Zbl 1301.30042)]. When the coefficients satisfy the normalization and quasireciprocity conditions, one can naturally extend the structure theory of seeds in the ordinary cluster algebras by Fomin and Zelevinsky to generalized cluster algebras. As the main result, we obtain formulas expressing cluster variables and coefficients in terms of \(c\)-vectors, \(g\)-vectors, and \(F\)-polynomials.

MSC:
13F60 Cluster algebras
Keywords:
cluster algebra
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