Nakanishi, Tomoki Structure of seeds in generalized cluster algebras. (English) Zbl 1366.13017 Pac. J. Math. 277, No. 1, 201-218 (2015). 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. Cited in 10 Documents MSC: 13F60 Cluster algebras Keywords:cluster algebra PDF BibTeX XML Cite \textit{T. Nakanishi}, Pac. J. Math. 277, No. 1, 201--218 (2015; Zbl 1366.13017) Full Text: DOI arXiv