A note on the paper "On Brlek-Reutenauer conjecture"

In this short note we point to an error in the proof of a theorem stated in [L. Balková & E. Pelantová & Š. Starosta, On BrlekReutenauer conjecture, Theoret. Comput. Sci. 412 (2011), 5649– 5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. Mathematics Subject Classification (2010): 68R15