We give a new combinatorial property of square factors in the infinite Thue-Morse word M2: every nontrivial factorization M2=w1w2 implies that w1 has a square suffix, or w2 has a square prefix. The proof is based on a coding which yields also a new demonstration of the characterization of square factors. Finally, we present results on the enumeration of factors: first explicit formulas, then the asymptotic values as well as a recurrence formula are given. © 1992.
Brlek, S. (1989). Enumeration of factors in the Thue-Morse word. Discrete Applied Mathematics, 24(1–3), 83–96. https://doi.org/10.1016/0166-218X(92)90274-E