On the permutation complexity of the Cantor-like sequences

• We obtain the permutation complexity of Cantor-like sequences.
• We give a precise recurrence relation for the permutation complexity of Cantor-like sequences.
• We give a generalized automaton for the first differences of the permutation of Cantor-like sequences.

In this paper, we give a precise formula for the permutation complexity of Cantor-like sequences, which are non-uniformly recurrent automatic sequences. Since the sequences are automatic, as it was proved by Charlier et al. in 2012, the permutation complexity of each of them is a regular sequence. We give a precise recurrence relation and a generalized automaton for it.