The lengths for which bicrucial square-free permutations exist [article]

Carla Groenland, Tom Johnston
2021 arXiv   pre-print
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:2109.00502v1 fatcat:u53yvcyyqze63mkaax3qadlfkm