Lyndon words with a fixed standard right factor

Frédérique Bassino (1) , Julien Clément (1) , Cyril Nicaud (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Given a totally ordered alphabet A = {a1 < a2 < < aq}, a Lyndon word is a word that is strictly smaller, for the lexicographical order, than any of its conjugates (i.e., all words obtained by a circular permutation on the letters). Lyndon words were introduced by Lyndon [6] under the name of "standard lexicographic sequences" in order to give a base for the free Lie algebra over A. The set of Lyndon words is denoted by L. For instance, with a binary alphabet A = {a, b}, the first Lyndon words until length five are L = {a, b, ab, aab, abb, aaab, aabb, abbb, aaaab, aaabb, aabab, aabbb, ababb, abbbb, . . . }. Note that a non-empty word is a Lyndon word if and only if it is strictly smaller than any of its proper suffixes.

Domaines: Algorithme et structure de données [cs.DS]

Frédérique Bassino, Julien Clément, Cyril Nicaud. Lyndon words with a fixed standard right factor. 15th ACM-SIAM Annual Symposium on Discrete Algorithms (SODA 2004), Jan 2004, New Orleans, Louisiana, United States. pp.646-647. ⟨hal-00619866⟩