Palindromic Subsequences in Finite Words

  • Clemens Müllner
  • Andrew RyzhikovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)


In 1999 Lyngsø and Pedersen proposed a conjecture stating that every binary circular word of length n with equal number of zeros and ones has an antipalindromic linear subsequence of length at least \(\frac{2}{3}n\). No progress over a trivial \(\frac{1}{2}n\) bound has been achieved since then. We suggest a palindromic counterpart to this conjecture and provide a non-trivial infinite series of circular words which prove the upper bound of \(\frac{2}{3}n\) for both conjectures at the same time. The construction also works for words over an alphabet of size k and gives rise to a generalization of the conjecture by Lyngsø and Pedersen. Moreover, we discuss some possible strengthenings and weakenings of the named conjectures. We also propose two similar conjectures for linear words and provide some evidences for them.


Palindrome Antipalindrome Circular words Subsequences 



We thank anonymous reviewers for their comments on the presentation of the paper. The second author is also grateful to András Sebő, Michel Rigo and Dominique Perrin for many useful discussions during the course of the work.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CNRS, Université Claude Bernard - Lyon 1VilleurbanneFrance
  2. 2.LIGM, Université Paris-EstMarne-la-ValléeFrance

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