On Collapsing Prefix Normal Words

  • Pamela FleischmannEmail author
  • Mitja Kulczynski
  • Dirk Nowotka
  • Danny Bøgsted Poulsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12038)


Prefix normal words are binary words in which each prefix has at least the same number of \(\mathsf {1}\)s as any factor of the same length. Firstly introduced in 2011, the problem of determining the index (amount of equivalence classes for a given word length) of the prefix normal equivalence relation is still open. In this paper, we investigate two aspects of the problem, namely prefix normal palindromes and so-called collapsing words (extending the notion of critical words). We prove characterizations for both the palindromes and the collapsing words and show their connection. Based on this, we show that still open problems regarding prefix normal words can be split into certain subproblems.



We would like to thank Florin Manea for helpful discussions and advice.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Pamela Fleischmann
    • 1
    Email author
  • Mitja Kulczynski
    • 1
  • Dirk Nowotka
    • 1
  • Danny Bøgsted Poulsen
    • 2
  1. 1.Department of Computer ScienceKiel UniversityKielGermany
  2. 2.Department of Computer ScienceAalborg UniversityAalborgDenmark

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