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arXiv · 2408.15390

Avoiding abelian and additive powers in rich words

Jonathan Andrade·Lucas Mol
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Abstract

This paper concerns the avoidability of abelian and additive powers in infinite rich words. In particular, we construct an infinite additive $5$-power-free rich word over $\{0,1\}$ and an infinite additive $4$-power-free rich word over $\{0, 1, 2\}$. The alphabet sizes are as small as possible in both cases, even for abelian powers.

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Jonathan Andrade, Lucas Mol. 2025-02-14. Avoiding abelian and additive powers in rich words. https://arxiv.org/abs/2408.15390

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