4 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…
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…
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…