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.^[1]

Formally, an infinite sequence of words w(n) is locally catenative if, for some positive integers k and i₁,...i_k:

${\displaystyle w(n)=w(n-i_{1})w(n-i_{2})\ldots w(n-i_{k}){\text{ for }}n\geq \max\{i_{1},\ldots ,i_{k}\}\,.}$

Some authors use a slightly different definition in which encodings of previous words are allowed in the concatenation.^[2]