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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.02121 |
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| _version_ | 1866912686712815616 |
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| author | Matveeva, Anastasia |
| author_facet | Matveeva, Anastasia |
| contents | We investigate the arithmetic nature of P-recursive sequences through the lens of their D-finite generating functions. Building on classical tools from differential algebra, we revisit the integrality criterion for Motzkin-type sequences due to Klazar and Luca, and propose a unified method for analysing global boundedness and algebraicity within a broader class of holonomic sequences. The central contribution is an algorithm that determines whether all, none, or a one-dimensional family of solutions to certain second-order recurrences are globally bounded. This approach generalizes earlier ad hoc methods and applies successfully to several well-known sequences from the On-Line Encyclopedia of Integer Sequences (OEIS). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the integrality of some P-recursive sequences Matveeva, Anastasia Number Theory Symbolic Computation We investigate the arithmetic nature of P-recursive sequences through the lens of their D-finite generating functions. Building on classical tools from differential algebra, we revisit the integrality criterion for Motzkin-type sequences due to Klazar and Luca, and propose a unified method for analysing global boundedness and algebraicity within a broader class of holonomic sequences. The central contribution is an algorithm that determines whether all, none, or a one-dimensional family of solutions to certain second-order recurrences are globally bounded. This approach generalizes earlier ad hoc methods and applies successfully to several well-known sequences from the On-Line Encyclopedia of Integer Sequences (OEIS). |
| title | On the integrality of some P-recursive sequences |
| topic | Number Theory Symbolic Computation |
| url | https://arxiv.org/abs/2511.02121 |