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Bibliographic Details
Main Authors: Melesio, Daniel Pérez, Simental, José
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.04614
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Table of Contents:
  • 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 $\mathbb{F} \not\cong \mathbb{F}_2$.