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Friezes and a construction of the euclidean cluster variables

Let $Q$ be an euclidean quiver. Using friezes in the sense of Assem-Reutenauer-Smith, we provide an algorithm for computing the (canonical) cluster character associated to any object in the cluster category of $Q$. In particular, this algorithm allows to compute all the cluster variables in the cluster algebra associated to $Q$. It also allows to compute the sum of the Euler characteristics of the quiver grassmannians of any module $M$ over the path algebra of $Q$.

preprint2010arXivOpen access
I. AssemG. Dupont
math.RTmath.RA
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I. AssemG. Dupont

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