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Ternary Square-Free Partial Words with Many Wildcards

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Developments in Language Theory (DLT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9840))

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Abstract

We contribute to the study of square-free words. The classical notion of a square-free word has a natural generalization to partial words, studied in several papers since 2008. We prove that the maximal density of wildcards in the ternary infinite square-free partial word is surprisingly big: 3/16. In addition, we introduce a related characteristic of infinite square-free words, called flexibility, and find its values for some interesting words and classes of words.

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Notes

  1. 1.

    As mentioned above, some sets do not have density; to avoid additional notions we postulate that upper (lower) bounds on flexibility should work for upper (resp., lower) densities of the corresponding wildcard sets.

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Author information

Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    Daniil Gasnikov & Arseny M. Shur

Authors
  1. Daniil Gasnikov
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  2. Arseny M. Shur
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Corresponding author

Correspondence to Arseny M. Shur .

Editor information

Editors and Affiliations

  1. Université du Québec à Montréal , Montreal, Québec, Canada

    Srečko Brlek

  2. Dept Mathematiques, Univ du Quebec Montreal Dept Mathematiques, Montreal, Québec, Canada

    Christophe Reutenauer

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Gasnikov, D., Shur, A.M. (2016). Ternary Square-Free Partial Words with Many Wildcards. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_15

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  • DOI: https://doi.org/10.1007/978-3-662-53132-7_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53131-0

  • Online ISBN: 978-3-662-53132-7

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