Locally catenative sequence: Difference between revisions

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In [[mathematics]], a '''locally catenative sequence''' is a sequence of [[word (mathematicsformal language theory)|words]] in which each word can be constructed as the concatenation of previous words in the sequence.<ref>{{cite book

| last = Rozenberg

| first = Grzegorz

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:<math>S(n)=S(n-1)S(n-2) \text{ for } n \ge 2 \, .</math>

The sequence of [[Thue-MorseThue–Morse sequence|Thue-MorseThue–Morse words]] ''T''(''n'') is not locally catenative by the first definition. However, it is locally catenative by the second definition because

:<math>T(n)=T(n-1)\mu(T(n-1)) \text{ for } n \ge 1 \, ,</math>

where the encoding ''&mu;'' replaces 0 with 1 and 1 with &nbsp;0.

==References==