Palindromic Periodicities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913337706545152 |
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| author | Simpson, Jamie |
| author_facet | Simpson, Jamie |
| contents | A palindromic periodicity is a factor of an infinite word $(ps)^ω$ where $p$ and $s$ are palindromes and the factor has length at least $|ps|$, for example, $accabaccab$. In this paper we describe several ways in which a palindromic periodicity may arise through the interaction of palindromes and periodicity, the simplest case being when a palindrome is itself periodic. We then consider what happens when a word is a palindromic periodicity in two ways, a situation similar to that considered in the Fine and Wilf Lemma and obtain something slightly stronger than that lemma. The paper ends with suggestions for further work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Palindromic Periodicities Simpson, Jamie Combinatorics 05A05 A palindromic periodicity is a factor of an infinite word $(ps)^ω$ where $p$ and $s$ are palindromes and the factor has length at least $|ps|$, for example, $accabaccab$. In this paper we describe several ways in which a palindromic periodicity may arise through the interaction of palindromes and periodicity, the simplest case being when a palindrome is itself periodic. We then consider what happens when a word is a palindromic periodicity in two ways, a situation similar to that considered in the Fine and Wilf Lemma and obtain something slightly stronger than that lemma. The paper ends with suggestions for further work. |
| title | Palindromic Periodicities |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2402.05381 |