Equations Enforcing Repetitions Under Permutations

  • Joel D. Day
  • Pamela Fleischmann
  • Florin Manea
  • Dirk Nowotka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)


The notion of repetition of factors in words is central to combinatorics on words. A recent generalisation of this concept considers repetitions under permutations: give an alphabet \(\Sigma \) and a morphism or antimorphism f on \(\Sigma ^*\), whose restriction to \(\Sigma \) is a permutation, w is an [f]-repetition if there exists \(\gamma \in \Sigma ^*\) such that \(w=f^{i_1}(\gamma )f^{i_2}(\gamma )\cdots f^{i_k}(\gamma )\), for some \(k\ge 2\). In this paper, we extend a series of classical repetition enforcing word equations to this general setting to obtain a series of word equations whose solutions are [f]-repetitions.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Joel D. Day
    • 1
  • Pamela Fleischmann
    • 1
  • Florin Manea
    • 1
  • Dirk Nowotka
    • 1
  1. 1.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany

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