Primitive Words and Lyndon Words in Automatic and Linearly Recurrent Sequences
Formal Languages and Automata Theory
2012-11-08 v3 Combinatorics
Abstract
We investigate questions related to the presence of primitive words and Lyndon words in automatic and linearly recurrent sequences. We show that the Lyndon factorization of a k-automatic sequence is itself k-automatic. We also show that the function counting the number of primitive factors (resp., Lyndon factors) of length n in a k-automatic sequence is k-regular. Finally, we show that the number of Lyndon factors of a linearly recurrent sequence is bounded.
Keywords
Cite
@article{arxiv.1207.5124,
title = {Primitive Words and Lyndon Words in Automatic and Linearly Recurrent Sequences},
author = {Daniel Goc and Kalle Saari and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1207.5124},
year = {2012}
}