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International Conference on Combinatorics on Words

WORDS 2019: Combinatorics on Words pp 93–105Cite as

Repetitions in Infinite Palindrome-Rich Words

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11682))

Abstract

Rich words are those containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We consider lower bounds on the repetition threshold of infinite rich words over 2- and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet \(\varSigma _2=\{0,1\}\) with a small critical exponent of \(2+\sqrt{2}/2\). This represents the first progress on an open problem of Vesti from 2017.

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Notes

  1. 1.

    Repository: https://github.com/aseemrb/Walnut/.

  2. 2.

    URL: https://github.com/aseemrb/Walnut/blob/master/Command Files/rich2.txt.

  3. 3.

    URL: https://github.com/aseemrb/research-scripts/blob/master/palindromes/palin.cpp.

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Acknowledgments

We are grateful to the referees for their suggestions.

After our paper was submitted, we learned from Edita Pelantová that our word r is a complementary symmetric Rote word [21], and hence by [3, 18] it follows that \(\mathbf r\) is rich.

Author information

Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Aseem R. Baranwal & Jeffrey Shallit

Authors
  1. Aseem R. Baranwal
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  2. Jeffrey Shallit
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Correspondence to Aseem R. Baranwal .

Editor information

Editors and Affiliations

  1. Loughborough University, Loughborough, UK

    Robert Mercaş

  2. Loughborough University, Loughborough, UK

    Daniel Reidenbach

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Baranwal, A.R., Shallit, J. (2019). Repetitions in Infinite Palindrome-Rich Words. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-28796-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28795-5

  • Online ISBN: 978-3-030-28796-2

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