arXiv:2410.14554 Abstract | arXiv Analytics

arXiv:2410.14554 [math.CO]Abstract References Reviews Resources

A determinantal formula for cluster variables in cluster algebras from surfaces

Published 2024-10-18Version 1

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.

Comments: 8 pages, 2 figures

Categories: math.CO

Subjects: 13F60, 05C70, 05C22

Keywords: cluster variables, cluster algebras, perfect matchings, simple determinantal formula, weighted biadjacency matrix

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