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• W2014076324 abstract "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-polynomials have constant term equal to 1. As an application, we compute the Euler-Poincare characteristic of quiver Grassmannians in Dynkin type $A$ and affine Dynkin type $tilde A$." @default.
• W2014076324 created "2016-06-24" @default.
• W2014076324 creator A5074585215 @default.
• W2014076324 date "2008-09-15" @default.
• W2014076324 modified "2023-09-27" @default.
• W2014076324 title "On cluster algebras arising from unpunctured surfaces II" @default.
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