140 citations · 1.3k across the 89 of their papers we have counts for
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Spectra of non-commutative dynamical systems and graphs related to fractal groups
Laurent Bartholdi, Rostislav I. Grigorchuk
We study spectra of noncommutative dynamical systems, representations of fractal groups, and regular graphs. We explicitly compute these spectra for five examples of groups acting…
The Growth of Grigorchuk's Group
Laurent Bartholdi
In 1980 Rostislav Grigorchuk constructed a group of intermediate growth, and later obtained the following estimates on its growth function: $$e^{\sqrt{n}}\precsimγ(n)\precsim e…
L-presentations and branch groups
Laurent Bartholdi
We introduce L-presentations: group presentations given by a generating set, a set of relations and a set of substitution rules on the generating set producing more relations. We f…
On the Word and Period Growth of some Groups of Tree Automorphisms
Laurent Bartholdi, Zoran Sunik
We generalize a class of groups defined by Rostislav Grigorchuk to a much larger class of groups, and provide upper and lower bounds for their word growth (they are all of intermed…
Lie Methods in Growth of Groups and Groups of Finite Width
Laurent Bartholdi, Rostislav I. Grigorchuk
In the first, mostly expository, part of this paper, a graded Lie algebra is associated to every group G given with an N-series of subgroups. The asymptotics of the Poincare series…