A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type |
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Authors: | Gregg Musiker |
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Institution: | (1) Institut de Math?matiques de Jussieu, UMR 7586 du CNRS, Universit? Paris 7-Denis Diderot, Case 7012, 2, place Jussieu, 75251 Paris Cedex 05, France |
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Abstract: | In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster
algebras of finite type with bipartite seed. 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. |
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Keywords: | |
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