A determinantal formula for cluster variables in cluster algebras from surfaces
Combinatorics
2025-11-06 v2
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.
Keywords
Cite
@article{arxiv.2410.14554,
title = {A determinantal formula for cluster variables in cluster algebras from surfaces},
author = {Javier De Loera},
journal= {arXiv preprint arXiv:2410.14554},
year = {2025}
}
Comments
10 pages, 2 figures. Typos corrected, added definitions 3.2, 3.4, 3.5, corrected sign in proposition 3.3