Binary patterns in the Prouhet-Thue-Morse sequence

Jorge Almeida, Ondřej Klíma

We show that, with the exception of the words $a^{2}b{a}^2$ and $b^{2}a{b}^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that seq…