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.{{cite book

| last = Rozenberg

| first = Grzegorz

|author2=Salomaa, Arto

| title = Handbook of Formal Languages

| publisher = Springer

| date = 1997

| pages = 262

| isbn = 3-540-60420-0}}

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

:$w(n)=w(n-i\_1)w(n-i\_2)\backslash ldots\; w(n-i\_k)\; \backslash text\{\; for\; \}\; n\; \backslash ge\; \backslash max\backslash \{i\_1,\; \backslash ldots,\; i\_k\backslash \}\; \backslash ,\; .$

Some authors use a slightly different definition in which encodings of previous words are allowed in the concatenation.{{cite book

| last = Allouche

| first = Jean-Paul

|author2=Shallit, Jeffrey

| title = Automatic Sequences

| publisher = Cambridge

| date = 2003

| pages = 237

| isbn = 0-521-82332-3}}