ω-Lyndon words

Inverse Lyndon words and Inverse Lyndon factorizations of words

Motivated by applications to string processing, we introduce variants of the Lyndon factorization called inverse Lyndon factorizations. Their factors, named inverse Lyndon words, are in a class that strictly contains anti-Lyndon words, that is Lyndon words with respect to the inverse lexicographic order. We prove that any nonempty word w admits a canonical inverse Lyndon factorization, named IC...

Universal Lyndon Words

A word w over an alphabet Σ is a Lyndon word if there exists an order defined on Σ for which w is lexicographically smaller than all of its conjugates (other than itself). We introduce and study universal Lyndon words, which are words over an n-letter alphabet that have length n! and such that all the conjugates are Lyndon words. We show that universal Lyndon words exist for every n and exhibit...

Partially Commutative Lyndon Words

Infinite Smooth Lyndon Words

Motivation Outline Notation Lyndon words Smooth words Result Idea of the proof Case a) Case b) Case c) Case d) Open problems Motivation ◮ Lyndon words : class of words having lexicographical order properties. ◮ Smooth words : class of words, related to the Kolakoski word, that can be easily compressed. ◮ Some infinite smooth words are also Lyndon words.

Suffixes, Conjugates and Lyndon Words