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Bulletin of the Australian Mathematical Society
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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https://dx.doi.org/10.48550/ar...
Article . 2024
License: CC BY
Data sources: Datacite
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RUNS IN PAPERFOLDING SEQUENCES

Authors: JEFFREY SHALLIT;

RUNS IN PAPERFOLDING SEQUENCES

Abstract

Abstract The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note, we observe that the sequence of run lengths in such a sequence, as well as the starting and ending positions of the nth run, is $2$ -synchronised and hence computable by a finite automaton. As a specific consequence, we obtain the recent results of Bunder, Bates and Arnold [‘The summed paperfolding sequence’, Bull. Aust. Math. Soc.110 (2024), 189–198] in much more generality, via a different approach. We also prove results about the critical exponent and subword complexity of these run-length sequences.

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Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Combinatorics, Discrete Mathematics, Formal Languages and Automata Theory (cs.FL), FOS: Mathematics, Combinatorics (math.CO), Formal Languages and Automata Theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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