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arXiv · 2401.14231

Strongly k-recursive sequences

Daniel Krenn·Jeffrey Shallit
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Abstract

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.

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Daniel Krenn, Jeffrey Shallit. 2024-01-25. Strongly k-recursive sequences. https://arxiv.org/abs/2401.14231

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