On Cluster Algebras Arising from Unpunctured Surfaces Ii

  title={On Cluster Algebras Arising from Unpunctured Surfaces Ii},
  author={Ralf Schiffler},
We study cluster algebras with principal and arbitrary coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of certain paths on a triangulation of the surface. As an immediate consequence, we prove the positivity conjecture of Fomin and Zelevinsky for these cluster algebras. Furthermore, we obtain direct formulas for F -polynomials and g-vectors and show that F… CONTINUE READING
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