Locally catenative sequence
Formally, an infinite sequence of words w(n) is locally catenative if, for some positive integers k and i1,...ik:
Some authors use a slightly different definition in which encodings of previous words are allowed in the concatenation.
The sequence of Fibonacci words S(n) is locally catenative because
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
where the encoding μ replaces 0 with 1 and 1 with 0.