1 citations · 1 across the 9 of their papers we have counts for
12 papers
On the word problem for just infinite groups
Alexey Talambutsa
We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable f…
On orbit sets generated by semigroups of one-dimensional affine functions
Karim F. Shamazov, Alexey L. Talambutsa
The one-dimensional orbit set is formed by the images of a number under the action of a semigroup generated by integer affine functions …
Unique expansions in number systems via refinement equations
Sergei V. Konyagin, Vladimir Yu. Protasov, Alexey L. Talambutsa
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the -ary number system with a set of non-negative i…
A simple algorithm for checking equivalence of counting functions on free monoids
Petr Kiyashko, Alexey Talambutsa
In this note we propose a new algorithm for checking whether two counting functions on a free monoid of rank are equivalent modulo a bounded function. The previously know…
The symmetric Post Correspondence Problem, and errata for the freeness problem for matrix semigroups
J. C. Birget, A. L. Talambutsa
We define the symmetric Post Correspondence Problem (PCP) and prove that it is undecidable. As an application we show that the original proof of undecidability of the freeness prob…
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…
Relations between counting functions on free groups and free monoids
Tobias Hartnick, Alexey Talambutsa
We consider finite sums of counting functions on the free group and the free monoid for . Two such sums are considered equivalent if they differ by a bounded…
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…