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On Infinite Prefix Normal Words

  • Ferdinando Cicalese
  • Zsuzsanna Lipták
  • Massimiliano RossiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

Prefix normal words are binary words that have no factor with more 1s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipták, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.

Keywords

Combinatorics on words Prefix normal words Infinite words Sturmian words Abelian complexity Paperfolding word Thue-Morse sequence Lexicographic order 

Notes

Acknowledgements

We wish to thank the participants of the Workshop on Words and Complexity (Lyon, February 2018), for interesting discussions and pointers, and to Péter Burcsi, who first got us interested in Sturmian words.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
  • Zsuzsanna Lipták
    • 1
  • Massimiliano Rossi
    • 1
    Email author
  1. 1.Dipartimento di InformaticaUniversity of VeronaVeronaItaly

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