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

Shuo Li, Jakub Pachocki, Jakub Radoszewski

A \emph{power} is a word of the form $\underset{k\text{times}}{\underbrace{uu...u}}$, where $u$ is a word and $k$ is a positive integer; the power is also called a {\em $k$-power} and $k…