Permutation Complexity of the Thue-Morse Word
Steven Widmer
TL;DR
This paper explores the combinatorial complexity of the infinite permutation derived from the Thue-Morse word, providing a formula based on pattern analysis and morphism actions.
Contribution
It introduces a formula for the permutation complexity of the Thue-Morse word by analyzing subpermutation patterns and morphism effects.
Findings
Established a formula for permutation complexity
Analyzed subpermutation patterns in Thue-Morse
Studied the action of the Thue-Morse morphism
Abstract
Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated with the well-known and well-studied Thue-Morse word. A formula for the complexity is established by studying patterns in subpermutations and the action of the Thue-Morse morphism on the subpermutations.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals