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Communication Dans Un Congrès Année : 2019

Palindromic Subsequences in Finite Words

Résumé

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 2/3 n. No progress over a trivial 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 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.

Dates et versions

hal-02942497 , version 1 (18-09-2020)

Identifiants

Citer

Clemens Müllner, Andrew Ryzhikov. Palindromic Subsequences in Finite Words. LATA 2019, Mar 2019, Saint Petersburg, Russia. pp.460-468, ⟨10.1007/978-3-030-13435-8_34⟩. ⟨hal-02942497⟩
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