A new factorization of the generalized period-doubling sequences through kernel words and gaps sequences
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911287325229056 |
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| author | Bognini, K. Ernest Ammar, Hamdi |
| author_facet | Bognini, K. Ernest Ammar, Hamdi |
| contents | In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of period-doubling sequences and demonstrate how to factorize a binary sequence using its kernel words. Next, we define gap sequences for period-doubling sequences and explore their relationship with kernel words. Lastly, we present a factorization of period-doubling sequences for $k\geq 3$ based on kernel words and gap sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new factorization of the generalized period-doubling sequences through kernel words and gaps sequences Bognini, K. Ernest Ammar, Hamdi Combinatorics 11B85, 37B10, 68Q45, 68R15 In this paper, we study some new factorizations of period-doubling sequences over a $k$-letter alphabet, where $k\geq 2$. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of period-doubling sequences and demonstrate how to factorize a binary sequence using its kernel words. Next, we define gap sequences for period-doubling sequences and explore their relationship with kernel words. Lastly, we present a factorization of period-doubling sequences for $k\geq 3$ based on kernel words and gap sequences. |
| title | A new factorization of the generalized period-doubling sequences through kernel words and gaps sequences |
| topic | Combinatorics 11B85, 37B10, 68Q45, 68R15 |
| url | https://arxiv.org/abs/2511.20881 |