Strongly k-recursive sequences
Formal Languages and Automata Theory
2024-01-26 v1 Discrete Mathematics
Combinatorics
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 -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.
Cite
@article{arxiv.2401.14231,
title = {Strongly k-recursive sequences},
author = {Daniel Krenn and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2401.14231},
year = {2024}
}