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Repetitions in Infinite Palindrome-Rich Words

  • Aseem R. BaranwalEmail author
  • Jeffrey Shallit
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Critical exponent Repetitions Rich words Palindrome 
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Notes

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.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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