The LyndonFactors(w) command produces the Lyndon factorization of the string w.

A word (string) w is a Lyndon word if it is aperiodic and is the lexicographically least member of its conjugacy class (which is the set of all rotations of w). Every word admits an unique factorization as a product (catenation) of a non-increasing sequence of Lyndon words, called its Lyndon factorization.

All of the StringTools package commands treat strings as (null-terminated) sequences of $8$-bit (ASCII) characters.  Thus, there is no support for multibyte character encodings, such as unicode encodings.

$\mathrm{with}\left(\mathrm{StringTools}\right)\:$

$\mathrm{LyndonFactors}\left(''abc''\right)$

$\left[''abc''\right]$

$\mathrm{LyndonFactors}\left(''abcdedcccbabab''\right)$

$\left[''abcdedcccb''\,''ab''\,''ab''\right]$

$\mathrm{LyndonFactors}\left(\mathrm{ThueMorse}\left(60\right)\right)$

$\left[''011''\,''01''\,''0011''\,''00101101''\,''0010110011010011''\,''001011001101001011010011''\,''001''\right]$

$\mathrm{LyndonFactors}\left(\mathrm{Fibonacci}\left(8\right)\right)$

$\left[''01''\,''00101''\,''0010010100101''\,''00100101''\,''001''\,''001''\right]$