Abstract
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 Tγthat 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 Tγ.
Original language | English (US) |
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Title of host publication | FPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics |
Pages | 673-684 |
Number of pages | 12 |
State | Published - Dec 1 2009 |
Event | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria Duration: Jul 20 2009 → Jul 24 2009 |
Other
Other | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 |
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Country/Territory | Austria |
City | Linz |
Period | 7/20/09 → 7/24/09 |
Keywords
- Cluster algebra
- F-polynomial
- Height function
- Principal coefficients
- Snake graphs
- Triangulated surface