Generating Lyndon brackets.: An addendum to: Fast algorithms to generate necklaces, unlabeled necklaces and irreducible polynomials over GF(2)

It is well known that the Lyndon words of length n can be used to construct a basis for the n-th 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 n-th 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).