On Growth and Fluctuation of k-Abelian Complexity

  • Julien Cassaigne
  • Juhani Karhumäki
  • Aleksi Saarela
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9139)


An extension of abelian complexity, so called k-abelian complexity, has been considered recently in a number of articles. This paper considers two particular aspects of this extension: First, how much the complexity can increase when moving from a level k to the next one. Second, how much the complexity of a given word can fluctuate. For both questions we give optimal solutions.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Julien Cassaigne
    • 1
  • Juhani Karhumäki
    • 2
  • Aleksi Saarela
    • 2
  1. 1.Institut de Mathmatiques de LuminyMarseille Cedex 9France
  2. 2.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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