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

A \emph{power} is a word of the form $\underbrace{uu...u}_{k \;\text{times}}$, where $u$ is a word and $k$ is a positive integer; the power isalso called a {\em $k$-power} and $k$ is its {\em exponent}. We prove that forany $k \ge 2$, the maximum number of different non-empty $k$-power factors in aword of length $n$ is between $\frac{n}{k-1}-\Theta(\sqrt{n})$ and$\frac{n-1}{k-1}$. We also show that the maximum number of different non-emptypower factors of exponent at least 2 in a length-$n$ word is at most $n-1$.Both upper bounds generalize the recent upper bound of $n-1$ on the maximumnumber of different square factors in a length-$n$ word by Brlek and Li (2022).

A note on the maximum number of $k$-powers in a finite word