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

Every finitely generated self-similar group naturally produces an infinitesequence of finite $d$-regular graphs $\Gamma_n$. We construct self-similargroups, whose graphs $\Gamma_n$ can be represented as an iterated zig-zagproduct and graph powering:$\Gamma_{n+1}=\Gamma_n^k\mathop{\mbox{\textcircled{$z$}}}\Gamma$ ($k\geq 1$).Also we construct self-similar groups, whose graphs $\Gamma_n$ can berepresented as an iterated replacement product and graph powering:$\Gamma_{n+1}=\Gamma_n^k\mathop{\mbox{\textcircled{$r$}}}\Gamma$ ($k\geq 1$).This gives simple explicit examples of self-similar groups, whose graphs$\Gamma_n$ form an expanding family, and examples of automaton groups, whosegraphs $\Gamma_n$ have linear diameters ${\rm diam}(\Gamma_n)=O(n)$ and boundedgirth.

Self-similar groups and the zig-zag and replacement products of graphs