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Privileged Factors in the Thue-Morse Word – A Comparison of Privileged Words and Palindromes

Jarkko Peltomäki, Privileged Factors in the Thue-Morse Word – A Comparison of Privileged Words and Palindromes. Discrete Applied Mathematics 193, 187–199, 2015.

http://dx.doi.org/10.1016/j.dam.2015.04.027

Abstract:

In this paper we study the privileged complexity function of the Thue–Morse word. We prove a recursive formula describing this function, and using the formula we show that the function is unbounded and that the values of the function have arbitrarily large gaps of zeros. This demonstrates that the privileged complexity function of an infinite word can drastically differ from its palindromic complexity function, even though there are relations between these functions. Further we study the behavior of palindromes and privileged words in infinite words and the relation between rich words and privileged words.

BibTeX entry:

@ARTICLE{jPeltomaki_Jarkko15b,
  title = {Privileged Factors in the Thue-Morse Word – A Comparison of Privileged Words and Palindromes},
  author = {Peltomäki, Jarkko},
  journal = {Discrete Applied Mathematics},
  volume = {193},
  publisher = {Elsevier},
  pages = {187–199},
  year = {2015},
  keywords = {thue-morse word,palindrome,privileged word,return word,rich word},
  ISSN = {0166-218X},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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