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arXiv · 2409.01206

Bicrucial $k$-power-free permutations

Margarita Akhmejanova·Aiya Kuchukova·Alexandr Valyuzhenich·Ilya Vorobyev
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Abstract

In this work, we prove that for every $k\geq 3$ there exist arbitrarily long bicrucial $k$-power-free permutations. We also show that for every $k\geq 3$ there exist right-crucial $k$-power-free permutations of any length at least $(k-1)(2k+1)$.

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Margarita Akhmejanova, Aiya Kuchukova, Alexandr Valyuzhenich, Ilya Vorobyev. 2024-09-02. Bicrucial $k$-power-free permutations. https://arxiv.org/abs/2409.01206

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