The sequence of
Fibonacci words
S(
n) is locally catenative because :S(n)=S(n-1)S(n-2) \text{ for } n \ge 2 \, . The sequence of
Thue–Morse words T(
n) is not locally catenative by the first definition. However, it is locally catenative by the second definition because :T(n)=T(n-1)\mu(T(n-1)) \text{ for } n \ge 1 \, , where the encoding
μ replaces 0 with 1 and 1 with 0. ==References==