Additional Properties and Applications
Lyndon words have an application to the description of free Lie algebras, in constructing a basis for the homogeneous part of a given degree; this was Lyndon's original motivation for introducing these words. Lyndon words may be understood as a special case of Hall sets.
A theorem of Radford states that the algebra of polynomials of Lyndon words with rational coefficients is a shuffle algebra; that is, they form an algebra over a ring, with multiplication taken to be the shuffle operator.
Read more about this topic: Lyndon Word
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