Strongly k-recursive sequences
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929224206516224 |
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| author | Krenn, Daniel Shallit, Jeffrey |
| author_facet | Krenn, Daniel Shallit, Jeffrey |
| contents | Drawing inspiration from a recent paper of Heuberger, Krenn, and Lipnik, we define the class of strongly k-recursive sequences. We show that every k-automatic sequence is strongly $k$-recursive, therefore k-recursive, and discuss that the converse is not true.
We also show that the class of strongly k-recursive sequences is a proper subclass of the class of k-regular sequences, and we present some explicit examples. We then extend the proof techniques to answer the same question for the class of k-recursive sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly k-recursive sequences Krenn, Daniel Shallit, Jeffrey Formal Languages and Automata Theory Discrete Mathematics Combinatorics Drawing inspiration from a recent paper of Heuberger, Krenn, and Lipnik, we define the class of strongly k-recursive sequences. We show that every k-automatic sequence is strongly $k$-recursive, therefore k-recursive, and discuss that the converse is not true. We also show that the class of strongly k-recursive sequences is a proper subclass of the class of k-regular sequences, and we present some explicit examples. We then extend the proof techniques to answer the same question for the class of k-recursive sequences. |
| title | Strongly k-recursive sequences |
| topic | Formal Languages and Automata Theory Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2401.14231 |