Linear recurrence relations for cluster variables of affine quivers

TL;DR

This paper proves that cluster variables in affine quivers follow linear recurrence relations, confirming a recent conjecture and advancing understanding of cluster algebra structures.

Contribution

It establishes that frieze sequences of cluster variables for affine quivers satisfy linear recurrences, providing a proof for a conjecture by Assem-Reutenauer-Smith.

Findings

Cluster variables in affine quivers follow linear recurrence relations

Proof of a conjecture by Assem-Reutenauer-Smith

Advances understanding of cluster algebra dynamics

Abstract

We prove that the frieze sequences of cluster variables associated with the vertices of an affine quiver satisfy linear recurrence relations. In particular, we obtain a proof of a recent conjecture by Assem-Reutenauer-Smith.