Cluster Tori over $\mathbb{F}_2$, Hexagonal Moves on Triangulations, and Minimal Coverings of Cluster Manifolds
Abstract
We study cluster algebras over $\mathbb{F}_2$. By the Laurent phenomenon there is a map from the set of seeds of the cluster algebra to the corresponding cluster variety. We show that in type $A$, fibers of this map can be described in terms of certain edges of the universal polytope of triangulations of a polygon. Moreover, we show that there is a section of this map giving seeds whose corresponding cluster tori cover the cluster manifold over any field $\mathbb{F}$, but there are also sections giving seeds whose cluster tori do not cover the cluster manifold over any field $\mathbb{F} \not\cong \mathbb{F}_2$.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Topological and Geometric Data Analysis
Geometric and Algebraic Topology
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 3
- Publication date
- 3 July 2026
- Language
- EN