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- W4281397211 abstract "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 is also called a {em $k$-power} and $k$ is its {em exponent}. We prove that for any $k ge 2$, the maximum number of different non-empty $k$-power factors in a word 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-empty power 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 maximum number of different square factors in a length-$n$ word by Brlek and Li (2022)." @default.
- W4281397211 created "2022-05-25" @default.
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- W4281397211 date "2022-05-20" @default.
- W4281397211 modified "2023-09-27" @default.
- W4281397211 title "A note on the maximum number of $k$-powers in a finite word" @default.
- W4281397211 doi "https://doi.org/10.48550/arxiv.2205.10156" @default.
- W4281397211 hasPublicationYear "2022" @default.
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