Abstract
In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type. In particular, we provide a family of graphs such that a weighted enumeration of their perfect matchings encodes the numerator of the associated Laurent polynomial while decompositions of the graphs correspond to the denominator. This complements recent work by Schiffler and Carroll-Price for a cluster expansion formula for the A n case while providing a novel interpretation for the B n, C n, and D n cases.
| Original language | English (US) |
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| Title of host publication | FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics |
| Pages | 435-446 |
| Number of pages | 12 |
| State | Published - Dec 1 2008 |
| Event | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: Jun 23 2008 → Jun 27 2008 |
Other
| Other | 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 |
|---|---|
| Country/Territory | Chile |
| City | Valparaiso |
| Period | 6/23/08 → 6/27/08 |
Keywords
- Classical type
- Cluster algebras
- Laurentness
- Perfect matchings
- Positivity