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.
A determinantal formula for cluster variables in cluster algebras from surfaces / De Loera Chavez, Javier Alejandro. - (2025).
A determinantal formula for cluster variables in cluster algebras from surfaces
Javier De Loera
Primo
2025
Abstract
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.File allegati a questo prodotto
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