4 citations · 7 across the 4 of their papers we have counts for
7 papers
Generic properties in some classes of automaton groups
Thibault Godin
We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such…
Numerical upper bounds on growth of automata groups
Jérémie Brieussel, Thibault Godin, Bijan Mohammadi
The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups,…
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…
An analogue to Dixon's theorem for automaton groups
Thibault Godin
Dixon's famous theorem states that the group generated by two random permutations of a finite set is generically either the whole symmetric group or the alternating group. In the c…
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…
On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata
Thibault Godin, Ines Klimann, Matthieu Picantin
This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers w…