0 O ct 2 00 8 CLUSTER EXPANSION FORMULAS AND PERFECT MATCHINGS
نویسنده
چکیده
We 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 GT,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 GT,γ .
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تاریخ انتشار 2008