Abstract
It is well known that the Lyndon words of length n can be used to construct a basis for the nth homogeneous component of the free Lie algebra. We develop an algorithm that uses a dynamic programming table to efficiently generate the standard bracketing for all Lyndon words of length n, thus constructing a basis for the nth homogeneous component of the free Lie algebra. The algorithm runs in linear amortized time; i.e., O( n) time per basis element. For a single Lyndon word, the table (and thus the standard bracketing) can be computed in time O( n 2).
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