Locally catenative sequence


In mathematics, a locally catenative sequence is a sequence of words in which each word can be constructed as the concatenation of previous words in the sequence.
Formally, an infinite sequence of words w 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.

Examples

The sequence of Fibonacci words S is locally catenative because
The sequence of Thue–Morse words T 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.