English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The growth of a finitely generated group is an important geometric invariantwhich has been studied for decades. It can be either polynomial, for awell-understood class of groups, or exponential, for most groups studied bygeometers, or intermediate, that is between polynomial and exponential. Despiterecent spectacular progresses, the class of groups with intermediate growthremains largely mysterious. Many examples of such groups are constructed usingMealy automata. The aim of this paper is to give an algorithmic procedure tostudy the growth of such automata groups, and more precisely to providenumerical upper bounds on their exponents. Our functions retrieve known optimalbounds on the famous first Grigorchuk group. They also improve known upperbounds on other automata groups and permitted us to discover several newexamples of automata groups of intermediate growth. All the algorithmsdescribed are implemented in GAP, a language dedicated to computational grouptheory.

Numerical upper bounds on growth of automata groups