Complexity of powers of a constant-recursive sequence
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913664739573760 |
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| author | Rowland, Eric Barron, Jesus Sistos |
| author_facet | Rowland, Eric Barron, Jesus Sistos |
| contents | Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms required for such a recurrence. For a constant-recursive sequence $s(n)$, we study the sequence $\left(\text{rank}\, s(n)^M\right)_{M\geq 1}$. We answer a question of Stinchcombe regarding the complexity of the powers of a constant-recursive sequence when the roots of the characteristic polynomial are not all distinct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity of powers of a constant-recursive sequence Rowland, Eric Barron, Jesus Sistos Number Theory Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms required for such a recurrence. For a constant-recursive sequence $s(n)$, we study the sequence $\left(\text{rank}\, s(n)^M\right)_{M\geq 1}$. We answer a question of Stinchcombe regarding the complexity of the powers of a constant-recursive sequence when the roots of the characteristic polynomial are not all distinct. |
| title | Complexity of powers of a constant-recursive sequence |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.14643 |