Enumeration of factors in the Thue-Morse word

Citations of this article
Mendeley users who have this article in their library.
Get full text


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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free