Geodesic
Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the $F$-polynomials called the $F$-matrices and show that the $F$-matrices have the self-duality which is analogous to the duality between the $C$- and $G$-matrices.
Keywords: cluster algebra, duality.
Mots-clés : mutation 
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     author = {Shogo Fujiwara and Yasuaki Gyoda},
     title = {Duality between {Final-Seed} and {Initial-Seed} {Mutations} in {Cluster} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a39/}
}
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Shogo Fujiwara; Yasuaki Gyoda. Duality between Final-Seed and Initial-Seed Mutations in Cluster Algebras. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a39/

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