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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Published in:arXiv.org 2024-10
Main Author: De Loera, Javier
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Language:English
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Clusters
Enumeration
Graphs
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description 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.
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subjects Clusters
Enumeration
Graphs
title A determinantal formula for cluster variables in cluster algebras from surfaces
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