Subgroup growth of virtually cyclic right-angled Coxeter groups and their free products

TL;DR

This paper calculates the asymptotic number of subgroups of a given index in virtually cyclic right-angled Coxeter groups and their free products, providing insights into their subgroup growth behavior.

Contribution

It provides the first detailed asymptotic enumeration of subgroups in these classes of Coxeter groups and their free products.

Findings

Asymptotic formulas for subgroup counts as index n grows large

Identification of growth rates for these groups

Extension of subgroup growth results to free products of Coxeter groups

Abstract

We determine the asymptotic number of index $n$ subgroups in virtually cyclic right-angled Coxeter groups and their free products as $n\to\infty$.