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Linear recurrence relations for cluster variables of affine quivers |
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| Authors: | Bernhard Keller Sarah Scherotzke |
| Institution: | aUniversité Paris Diderot – Paris 7, Institut Universitaire de France, UFR de Mathématiques, Institut de Mathématiques de Jussieu, UMR 7586 du CNRS, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France;bUniversité Paris Diderot – Paris 7, UFR de Mathématiques, Institut de Mathématiques de Jussieu, UMR 7586 du CNRS, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France |
| Abstract: | We prove that the frieze sequences of cluster variables associated with the vertices of an affine quiver satisfy linear recurrence relations. In particular, we obtain a proof of a recent conjecture by Assem–Reutenauer–Smith. |
| Keywords: | Cluster algebra Linear recurrence Frieze pattern Quiver representation |
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