On cluster algebras arising from unpunctured surfaces II |
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Authors: | Ralf Schiffler |
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Institution: | Department of Mathematics, University of Connecticut, 196 Auditorium Road, Storrs, CT 06269-3009, USA |
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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-Poincaré characteristic of quiver Grassmannians in Dynkin type A and affine Dynkin type . |
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Keywords: | 16G20 16G70 18E30 05E15 |
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