A determinantal formula for cluster variables in cluster algebras from surfaces

For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake grap...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Author: De Loera, Javier
Format: Article
Language:English
Subjects:
Clusters
Enumeration
Graphs
Online Access:Get full text
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Summary:For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weighted biadjacency matrix of the associated snake graphs, thus circumventing the enumeration of their perfect matchings.
ISSN:2331-8422