Bicrucial $k$-power-free permutations

Abstract

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