2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171981We study cluster algebras with principal 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 perfect matchings of a certain graph $G_{T,γ}$ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula for these Laurent polynomial expansions in terms of subgraphs of the graph $G_{T,γ}$.19 pages, 8 figuresRepresentation TheoryCombinatorics16S99; 05E99; 05C70text