Nyldon Factorization of Thue-Morse Words and Fibonacci Words
Data Structures and Algorithms
2025-09-12 v2 Discrete Mathematics
Abstract
The Nyldon factorization is a string factorization that is a non-decreasing product of Nyldon words. Nyldon words and Nyldon factorizations are recently defined combinatorial objects inspired by the well-known Lyndon words and Lyndon factorizations. In this paper, we investigate the Nyldon factorization of several words. First, we fully characterize the Nyldon factorizations of the (finite) Fibonacci and the (finite) Thue-Morse words. Moreover, we show that there exists a non-decreasing product of Nyldon words that is a factorization of the infinite Thue-Morse word.
Keywords
Cite
@article{arxiv.2507.23659,
title = {Nyldon Factorization of Thue-Morse Words and Fibonacci Words},
author = {Kaisei Kishi and Kazuki Kai and Yuto Nakashima and Shunsuke Inenaga and Hideo Bannai},
journal= {arXiv preprint arXiv:2507.23659},
year = {2025}
}
Comments
A full version of our conference paper accepted for SPIRE 2025