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On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We show the polynomial property of $F$-polynomials for generalized quantum cluster algebras and obtain the associated separation formulas under a mild condition. Along the way, we obtain Gupta's formulas of $F$-polynomials for generalized quantum cluster algebras. These formulas specialize to Gupta's formulas for quantum cluster algebras and cluster algebras respectively. Finally, a generalization of Gupta's formula has also been discussed in the setting of generalized cluster algebras.
Keywords: separation formula, Fock–Goncharov decomposition, generalized quantum cluster algebra, generalized cluster algebra.
Mots-clés : $F$-polynomial 
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     author = {Changjian Fu and Liangang Peng and Huihui Ye},
     title = {On $F${-Polynomials} for {Generalized} {Quantum} {Cluster} {Algebras} and {Gupta's} {Formula}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
     volume = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a79/}
}
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Changjian Fu; Liangang Peng; Huihui Ye. On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a79/

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