Lie complexity of words

Automatic sequences of rank two

“…We can also prove that k-automatic words are discrete, and even something more general. The following result appears in earlier work of the authors ( [4], Thm. 1.2) but we give a simpler and more self-contained proof here.…”

“…1.2) but we give a simpler and more self-contained proof here. We note, however, that the following proof does not recover the upper bound on the number of primitive factors that can occur with unbounded exponent (up to cyclic equivalence), which was given in [4].…”

“…Kobayashi and Otto [23] gave an efficient algorithm to test the repetitivity of a pure morphic word. Klouda and Starosta [20] showed further that every pure morphic word x is discrete, while the authors [4] proved that words of linear factor complexity are discrete.…”