Nyldon Factorization of Thue-Morse Words and Fibonacci Words
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916946518212608 |
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| author | Kishi, Kaisei Kai, Kazuki Nakashima, Yuto Inenaga, Shunsuke Bannai, Hideo |
| author_facet | Kishi, Kaisei Kai, Kazuki Nakashima, Yuto Inenaga, Shunsuke Bannai, Hideo |
| contents | The Nyldon factorization is a string factorization that is a non-decreasing product of Nyldon words. Nyldon words and Nyldon factorizations are recently defined combinatorial objects inspired by the well-known Lyndon words and Lyndon factorizations. In this paper, we investigate the Nyldon factorization of several words. First, we fully characterize the Nyldon factorizations of the (finite) Fibonacci and the (finite) Thue-Morse words. Moreover, we show that there exists a non-decreasing product of Nyldon words that is a factorization of the infinite Thue-Morse word. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nyldon Factorization of Thue-Morse Words and Fibonacci Words Kishi, Kaisei Kai, Kazuki Nakashima, Yuto Inenaga, Shunsuke Bannai, Hideo Data Structures and Algorithms Discrete Mathematics The Nyldon factorization is a string factorization that is a non-decreasing product of Nyldon words. Nyldon words and Nyldon factorizations are recently defined combinatorial objects inspired by the well-known Lyndon words and Lyndon factorizations. In this paper, we investigate the Nyldon factorization of several words. First, we fully characterize the Nyldon factorizations of the (finite) Fibonacci and the (finite) Thue-Morse words. Moreover, we show that there exists a non-decreasing product of Nyldon words that is a factorization of the infinite Thue-Morse word. |
| title | Nyldon Factorization of Thue-Morse Words and Fibonacci Words |
| topic | Data Structures and Algorithms Discrete Mathematics |
| url | https://arxiv.org/abs/2507.23659 |