Growth rate of cluster algebras

TL;DR

This paper completes the calculation of growth rates for cluster algebras, demonstrating that all exceptional non-affine mutation-finite cluster algebras grow exponentially.

Contribution

It provides a complete classification of growth rates for all exceptional non-affine mutation-finite cluster algebras, confirming their exponential growth.

Findings

All exceptional non-affine mutation-finite cluster algebras exhibit exponential growth.

The growth rate computation is now complete for these classes.

This advances understanding of the dynamics of cluster algebra mutations.

Abstract

We complete the computation of growth rate of cluster algebras. In particular, we show that growth of all exceptional non-affine mutation-finite cluster algebras is exponential.