36 citations · 99 across the 12 of their papers we have counts for
8 papers · 1 filter
Automatic semigroups vs automaton semigroups
Matthieu Picantin
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated…
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…
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…
Cyclic amalgams, HNN extensions, and Garside one-relator groups
Matthieu Picantin
Garside groups are a natural lattice-theoretic generalisation of the braid groups and spherical type Artin--Tits groups. Here we show that the class of Garside groups is closed und…
A new Garside structure for braid groups of type
Ruth Corran, Matthieu Picantin
We describe a new presentation for the complex reflection groups of type and their braid groups. A diagram for this presentation is proposed. The presentation is a monoid…
Garside monoids vs divisibility monoids
Matthieu Picantin
Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distr…