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arXiv · 2203.16742

On the number of $k$-powers in a finite word

Shuo Li
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Abstract

This note is an attempt to attack a conjecture of Fraenkel and Simpson stated in 1998 concerning the number of distinct squares in a finite word. By counting the number of (right-)special factors, we give an upper bound of the number of {\em $k$-powers} in a finite word for any integer $k\geq 3$. By {\em $k$-power}, we mean a word of the form $\underbrace{uu...u}_{k \; \text{times}}$.

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Shuo Li. 2022-03-31. On the number of $k$-powers in a finite word. https://arxiv.org/abs/2203.16742

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