The lengths for which bicrucial square-free permutations exist

Abstract

A square is a factor $S=(S_1;S_2)$ where $S_1$ and $S_2$ have the same pattern, and a permutation is said to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial if every extension to the left or right contains a square. We completely classify for which $n$ there exists a bicrucial square-free permutation of length $n$.

arXiv comment24 pages, 4 figures

References in corpus (2)

• S-crucial and bicrucial permutations with respect to squares
• No extremal square-free words over large alphabets