An Example of an Automatic Graph of Intermediate Growth

2013/12/13 by Alexei Miasnikov, Miasnikov, Alexei, Dmytro Savchuk +1
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1312.3710

openalex publication_date 2013/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of a 4-regular infinite automatic graph of intermediate growth. It is constructed as a Schreier graph of a certain group generated by 3-state automaton. The question was motivated by an open problem on the existence of Cayley automatic groups of intermediate growth.

Related

• Growth of groups with linear Schreier graphs
• An automata group of intermediate growth and exponential activity
• Cayley graphs and automatic sequences
• The Limit Space of Self-similar Groups and Schreier graphs
• Numerical upper bounds on growth of automata groups