62 citations · 151 across the 11 of their papers we have counts for
13 papers
A new hierarchy for automaton semigroups
Laurent Bartholdi, Thibault Godin, Ines Klimann +1
We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy…
To Infinity and Beyond
Ines Klimann
We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct conseque…
On level-transitivity and exponential growth
Ines Klimann
We prove that if the group generated by a Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growt…
Boundary action of automaton groups without singular points and Wang tilings
D. D'Angeli, Th. Godin, I. Klimann +2
We study automaton groups without singular points, that is, points in the boundary for which the map that associates to each point its stabilizer, is not continuous. This is motiva…
Connected reversible Mealy automata of prime size cannot generate infinite Burnside groups
Thibault Godin, Ines Klimann
The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automa…
Orbit automata as a new tool to attack the order problem in automaton groups
Ines Klimann, Matthieu Picantin, Dmytro Savchuk
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group on the subtrees corresponding to the orbits of on levels of the tree. T…