English

Bicrucial $k$-power-free permutations

Combinatorics 2024-09-04 v1

Abstract

In this work, we prove that for every k3k\geq 3 there exist arbitrarily long bicrucial kk-power-free permutations. We also show that for every k3k\geq 3 there exist right-crucial kk-power-free permutations of any length at least (k1)(2k+1)(k-1)(2k+1).

Cite

@article{arxiv.2409.01206,
  title  = {Bicrucial $k$-power-free permutations},
  author = {Margarita Akhmejanova and Aiya Kuchukova and Alexandr Valyuzhenich and Ilya Vorobyev},
  journal= {arXiv preprint arXiv:2409.01206},
  year   = {2024}
}
R2 v1 2026-06-28T18:31:29.071Z