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arXiv · 1003.0197

Friezes and a construction of the euclidean cluster variables

I. Assem·G. Dupont
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Abstract

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 $Q$.

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I. Assem, G. Dupont. 2010-02-28. Friezes and a construction of the euclidean cluster variables. https://arxiv.org/abs/1003.0197

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