Some Remarks on Palindromic Periodicities
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916352049020928 |
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| author | Fici, Gabriele Shallit, Jeffrey Simpson, Jamie |
| author_facet | Fici, Gabriele Shallit, Jeffrey Simpson, Jamie |
| contents | 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 $(ps)^ω= pspsps\cdots$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some Remarks on Palindromic Periodicities Fici, Gabriele Shallit, Jeffrey Simpson, Jamie Combinatorics Discrete Mathematics Formal Languages and Automata Theory 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 $(ps)^ω= pspsps\cdots$. 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. |
| title | Some Remarks on Palindromic Periodicities |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2407.10564 |