On cluster algebras arising from unpunctured surfaces II
| dc.creator | Schiffler, Ralf | |
| dc.date | 2008-09-15 | |
| dc.date | 2008-09-18 | |
| dc.date.accessioned | 2026-07-07T10:03:26Z | |
| dc.date.available | 2026-07-07T10:03:26Z | |
| dc.description | 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 $\tilde A$. | |
| dc.description | 36 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0809.2593 | |
| dc.identifier | http://arxiv.org/abs/0809.2593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169287 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S99; 05E99; 16G20 | |
| dc.title | On cluster algebras arising from unpunctured surfaces II | |
| dc.type | text |