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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let G be a group generated by $r$ elements $g_1,g_2,..., g_r.$ Among thereduced words in $g_1,g_2,..., g_r$ of length $n$ some, say $\gamma_n,$represent the identity element of the group $G.$ It has been shown in acombinatorial way that the $2n$th root of $\gamma_{2n}$ has a limit, called thecogrowth exponent with respect to generators $g_1,g_2,..., g_r.$ We show byanalytic methods that the numbers $\gamma_n$ vary regularly; i.e. the ratio$\gamma_{2n+2}/\gamma_{2n}$ is also convergent. Moreover we derive new preciseinformation on the domain of holomorphy of $\gamma(z),$ the generating functionassociated with the coefficients $\gamma_n.$

The ratio and generating function of cogrowth coefficients of finitely generated groups