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Similarity Relations and Repetition-Freeness

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Combinatorics on Words

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8079))

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Abstract

A similarity relation is a relation on words of equal length induced by a symmetric and reflexive relation on letters. The aim of this article is to give an overview of the results concerning repetition-freeness in connection with similarity relations. We consider so called chain relations, cyclic relations and partial words, which can be seen as a special case of similarity relations. As a new result, we prove that local 3 + -repetitions can be avoided in binary partial words and the local avoidability index of \(\mathring{R}\)-cubes is five, where \(\mathring{R}\) is a relation such that the graph of the relation is a cycle.

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Author information

Authors and Affiliations

  1. Department of Teacher Education, University of Turku, PO Box 175, 26101, Rauma, Finland

    Tomi Kärki

  2. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Tomi Kärki

Authors
  1. Tomi Kärki
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Editor information

Editors and Affiliations

  1. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  2. University of Turku, 20014, Turku, Finland

    Arto Lepistö

  3. FUNDIM, University of Turku, Finland

    Luca Zamboni

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Kärki, T. (2013). Similarity Relations and Repetition-Freeness. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds) Combinatorics on Words. Lecture Notes in Computer Science, vol 8079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40579-2_19

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  • DOI: https://doi.org/10.1007/978-3-642-40579-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40578-5

  • Online ISBN: 978-3-642-40579-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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