Nyldon words
Abstract
The Chen-Fox-Lyndon theorem states that every finite word over a fixed alphabet can be uniquely factorized as a lexicographically nonincreasing sequence of Lyndon words. This theorem can be used to define the family of Lyndon words in a recursive way. If the lexicographic order is reversed in this definition, we obtain a new family of words, which are called the Nyldon words. In this paper, we show that every finite word can be uniquely factorized into a lexicographically nondecreasing sequence of Nyldon words. Otherwise stated, Nyldon words form a complete factorization of the free monoid with respect to the decreasing lexicographic order. Then we investigate this new family of words. In particular, we show that Nyldon words form a right Lazard set.
Cite
@article{arxiv.1804.09735,
title = {Nyldon words},
author = {Émilie Charlier and Manon Philibert and Manon Stipulanti},
journal= {arXiv preprint arXiv:1804.09735},
year = {2019}
}
Comments
28 pages