| Issue |
RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1051/ita/2022003 | |
| Published online | 14 February 2022 | |
Critical factorisation in square-free words
Department of Mathematics and Statistics, University of Turku,
Turku, Finland.
* Corresponding author: harju@utu.fi
Received:
10
August
2021
Accepted:
28
January
2022
A position p in a word w is critical if the minimal local period at p is equal to the global period of w. According to the Critical Factorisation Theorem all words of length at least two have a critical point. We study the number η(w) of critical points of square-free ternary words w, i.e., words over a three letter alphabet. We show that the sufficiently long square-free words w satisfy η(w) ≤|w|− 5 where |w| denotes the length of w. Moreover, the bound |w|− 5 is reached by infinitely many words. On the other hand, every square-free word w has at least |w|∕4 critical points, and there is a sequence of these words closing to this bound.
Mathematics Subject Classification: 68R15
Key words: Critical point / critical factorisation theorem / ternary words / square-free words
© The authors. Published by EDP Sciences, 2022
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