RAIRO-Theor. Inf. Appl.
Volume 55, 2021
|Number of page(s)||15|
|Published online||20 January 2021|
Upper bound for palindromic and factor complexity of rich words
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague,
Prague 6, Czechia.
* Corresponding author: firstname.lastname@example.org
Accepted: 11 December 2020
A finite word w of length n contains at most n + 1 distinct palindromic factors. If the bound n + 1 is attained, the word w is called rich. An infinite word w is called rich if every finite factor of w is rich.
Let w be a word (finite or infinite) over an alphabet with q > 1 letters, let Facw(n) be the set of factors of length n of the word w, and let Palw(n) ⊆ Facw(n) be the set of palindromic factors of length n of the word w.
where w is an infinite word whose set of factors is closed under reversal. We prove this inequality for every finite word v with |v| ≥ n + 1 and v(n + 1) closed under reversal.
Mathematics Subject Classification: 68R15
Key words: Rich words / Palindromes / Palindromic complexity / Factor complexity
© EDP Sciences, 2021
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