On the number of k-powers in a finite word

Shuo Li

doi:10.1016/j.aam.2022.102371

On the number of k-powers in a finite word

Shuo Li

Université du Québec à Montréal

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 for the number of k-powers in a finite word for any integer k≥3. By k-power, we mean a word of the form uu...u︸ktimes.

Original language	English
Article number	102371
Journal	Advances in Applied Mathematics
Volume	139
DOIs	https://doi.org/10.1016/j.aam.2022.102371
State	Published - Aug 2022
Externally published	Yes

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10.1016/j.aam.2022.102371

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title = "On the number of k-powers in a finite word",

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 for the number of k-powers in a finite word for any integer k≥3. By k-power, we mean a word of the form uu...u︸ktimes.",

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AB - 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 for the number of k-powers in a finite word for any integer k≥3. By k-power, we mean a word of the form uu...u︸ktimes.

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On the number of k-powers in a finite word

Abstract

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