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arXiv · 1207.5124

Primitive Words and Lyndon Words in Automatic and Linearly Recurrent Sequences

Daniel Goc·Kalle Saari·Jeffrey Shallit
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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.

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Daniel Goc, Kalle Saari, Jeffrey Shallit. 2012-07-21. Primitive Words and Lyndon Words in Automatic and Linearly Recurrent Sequences. https://arxiv.org/abs/1207.5124

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