An automata group of intermediate growth and exponential activity
J\'er\'emie Brieussel
TL;DR
This paper introduces a new automata group exhibiting intermediate growth and exponential activity, generated by a 4-state automaton on an 8-letter alphabet, with a complex limit space.
Contribution
It provides a novel example of an automata group with intermediate growth and exponential activity, expanding understanding of automata groups' properties.
Findings
The group has intermediate growth.
The automaton has exponential activity.
Its limit space is not simply connected.
Abstract
We give a new example of an automata group of intermediate growth. It is generated by an automaton with 4 states on an alphabet with 8 letters. This automata group has exponential activity and its limit space is not simply connected.
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