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Cluster Expansion Formulas and Perfect Matchings by Musiker, Gregg; Schiffler, Ralf is a scholarly article available to read on EtoBox.

What is Cluster Expansion Formulas and Perfect Matchings about?

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 $G_{T,\gamma}$ 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 $G_{T,\gamma}$.

Author

Musiker, Gregg; Schiffler, Ralf

Published

2008

Language

EN