Rationality of the multivariate growth series for algebraic sets of virtually abelian groups

TL;DR

This paper proves that the multivariate relative growth series for algebraic sets within virtually abelian groups are rational functions, confirming a conjecture by Evetts and Levine.

Contribution

It establishes the rationality of the multivariate growth series for algebraic sets in virtually abelian groups, resolving a longstanding conjecture.

Findings

Confirmed the rationality of the growth series

Validated the conjecture by Evetts and Levine

Provides a new understanding of algebraic sets in virtually abelian groups

Abstract

We prove the rationality of the multivariate relative growth series for algebraic sets of virtually abelian groups, which had been conjectured by Evetts and Levine.