A characterization of binary morphisms generating Lyndon infinite words
Gwena\"el Richomme (ESCAPE, UPVM), Patrice S\'e\'ebold (ESCAPE, UPVM)
TL;DR
This paper characterizes binary morphisms that generate infinite Lyndon words, providing a clear criterion for when such morphisms produce these special infinite sequences.
Contribution
It offers a new characterization of binary endomorphisms that generate Lyndon infinite words, advancing understanding of their structure and generation.
Findings
Provides a characterization criterion for binary morphisms producing Lyndon infinite words
Identifies conditions under which binary endomorphisms generate Lyndon sequences
Enhances understanding of the structure of Lyndon infinite words
Abstract
An infinite word is an infinite Lyndon word if it is smaller, with respect to the lexicographic order, than all its proper suffixes, or equivalently if it has infinitely many finite Lyndon words as prefixes. A characterization of binary endomorphisms generating Lyndon infinite words is provided.
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