Nyldon Factorization of Thue-Morse Words and Fibonacci Words
Kaisei Kishi, Kazuki Kai, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai
TL;DR
This paper explores the Nyldon factorization of Fibonacci and Thue-Morse words, providing complete characterizations and demonstrating a non-decreasing Nyldon factorization of the infinite Thue-Morse sequence.
Contribution
It offers the first comprehensive analysis of Nyldon factorizations for these well-known words and establishes the existence of an infinite Nyldon factorization for Thue-Morse.
Findings
Complete Nyldon factorizations of finite Fibonacci words
Complete Nyldon factorizations of finite Thue-Morse words
Existence of a non-decreasing Nyldon factorization of the infinite Thue-Morse word
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.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Computability, Logic, AI Algorithms