Cluster expansion formulas and perfect matchings

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dc.creatorMusiker, Gregg
dc.creatorSchiffler, Ralf
dc.date2008-10-20
dc.date.accessioned2026-07-07T10:11:49Z
dc.date.available2026-07-07T10:11:49Z
dc.descriptionWe 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 $G_{T,γ}$.
dc.description19 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0810.3638
dc.identifierhttp://arxiv.org/abs/0810.3638
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171981
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject16S99; 05E99; 05C70
dc.titleCluster expansion formulas and perfect matchings
dc.typetext

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