Some Remarks on Palindromic Periodicities
<|reference_start|>Some Remarks on Palindromic Periodicities: We say a finite word $x$ is a palindromic periodicity if there exist two palindromes $p$ and $s$ such that $|x| \geq |ps|$ and $x$ is a prefix of the word $(ps)^\omega = pspsps\cdots$. In this paper we examine the palindromic periodicities occurring in some classical infinite words, such as Sturmian words, episturmian words, the Thue-Morse word, the period-doubling word, the Rudin-Shapiro word, the paperfolding word, and the Tribonacci word, and prove a number of results about them. We also prove results about words with the smallest number of palindromic periodicities.<|reference_end|>
@article{fici2024some,
    title={Some Remarks on Palindromic Periodicities},
    author={Gabriele Fici, Jeffrey Shallit, Jamie Simpson},
    journal={arXiv preprint arXiv:2407.10564},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10564},
    primaryClass={math.CO cs.DM cs.FL}
}