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Critical exponent of binary words with few distinct palindromes
Published 21 Nov 2023 in math.CO and cs.DM | (2311.13003v2)
Abstract: We study infinite binary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponents. This extends results by Fici and Zamboni [TCS 2013]. Interestingly, the words with 18 and 20 palindromes happen to be morphic images of the fixed point of the morphism $\texttt{0}\mapsto\texttt{01}$, $\texttt{1}\mapsto\texttt{21}$, $\texttt{2}\mapsto\texttt{0}$.
- L. Dvořáková, E. Pelantová. The repetition threshold of episturmian sequences. arXiv:2309.00988
- G. Fici and L.Q. Zamboni. On the least number of palindromes contained in an infinite word. Theoretical Computer Science 481 (2013), 1–8.
- L. Fleischer and J. Shallit. Words with few palindromes, revisited. arXiv:1911.12464
- A. Shur. Growth properties of power-free languages. Computer Science Review 6 (2012), 187–208.
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