6 papers
Efficient computations with counting functions on free groups and free monoids
Tobias Hartnick, Alexey Talambutsa
We present efficient algorithms to decide whether two given counting functions on non-abelian free groups or monoids are at bounded distance from each other and to decide whether t…
On free semigroups of affine maps on the real line
Alexander Kolpakov, Alexey Talambutsa
In this note we generalise some of the work of Klarner on free semigroups of affine maps acting on the real line by using a classical approach from geometric group theory (the Ping…
Growth rates of Coxeter groups and Perron numbers
Alexander Kolpakov, Alexey Talambutsa
We define a large class of abstract Coxeter groups, that we call --spanned, and for which the word growth rate and the geodesic growth rate appear to be Perron numbers. Thi…
Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers
Alexander Kolpakov, Alexey Talambutsa
We prove that for any infinite right-angled Coxeter or Artin group, its spherical and geodesic growth rates (with respect to the standard generating set) either take values in the…
Minimal exponential growth rates of metabelian Baumslag-Solitar groups and lamplighter groups
Michelle Bucher, Alexey Talambutsa
We prove that for any prime the minimal exponential growth rate of the Baumslag-Solitar group and the lamplighter group $\mathcal{L}_p=(\mathbb{Z}/p\mathbb{Z})\…
Exponential growth rates of free and amalgamated products
Michelle Bucher, Alexey Talambutsa
We prove that there is a gap between and for the exponential growth rate of free products not isomorphic to the infinite dihedral group. For ama…