On (almost) realizable subsequences of linearly recurrent sequences
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916168571289600 |
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| author | Luca, Florian Ward, Tom |
| author_facet | Luca, Florian Ward, Tom |
| contents | In this note we show that if $(u_n)_{n\geqslant 1}$ is a simple linearly recurrent sequence of integers whose minimal recurrence of order $k$ involves only positive coefficients that has positive initial terms, then $(Mu_{n^s})_{n\geqslant 1}$ is the sequence of periodic point counts for some map for a suitable positive integer $M$ and $s$ any sufficiently large multiple of $k!$. This extends a result of Moss and Ward [The Fibonacci Quarterly 60 (2022), 40-47] who proved the result for the Fibonacci sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02711 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On (almost) realizable subsequences of linearly recurrent sequences Luca, Florian Ward, Tom Number Theory Dynamical Systems 11B50, 37P35 In this note we show that if $(u_n)_{n\geqslant 1}$ is a simple linearly recurrent sequence of integers whose minimal recurrence of order $k$ involves only positive coefficients that has positive initial terms, then $(Mu_{n^s})_{n\geqslant 1}$ is the sequence of periodic point counts for some map for a suitable positive integer $M$ and $s$ any sufficiently large multiple of $k!$. This extends a result of Moss and Ward [The Fibonacci Quarterly 60 (2022), 40-47] who proved the result for the Fibonacci sequence. |
| title | On (almost) realizable subsequences of linearly recurrent sequences |
| topic | Number Theory Dynamical Systems 11B50, 37P35 |
| url | https://arxiv.org/abs/2204.02711 |