# Discrete Mathematics & Theoretical Computer Science

## Volume 1 n° 1 (1997), pp. 101-114

author: | Philippe Andary |
---|---|

title: | Finely homogeneous computations in free Lie algebras |

keywords: | Lie algebras, finely homogeneous computations |

abstract: | We first give a fast algorithm to compute the maximal Lyndon word (with respect to lexicographic order) of Ly-alpha(A) for every given multidegree alpha in Nk. We then give an algorithm to compute all the words living in Ly-alpha(A) for any given alpha in Nk. The best known method for generating Lyndon words is that of Duval [1], which gives a way to go from every Lyndon word of length n to its successor (with respect to lexicographic order by length), in space and worst case time complexity O(n). Finally, we give a simple algorithm which uses Duval’s method (the one above) to compute the next standard bracketing of a Lyndon word for lexicographic order by length. We can find an interesting application of this algorithm in control theory, where one wants to compute within the command Lie algebra of a dynamical system (letters are actually vector fields). |

reference: | Philippe Andary (1997),
Finely homogeneous computations in free Lie algebras,
Discrete Mathematics and Theoretical Computer Science 1, pp. 101-114 |

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