Permutation Complexity Related to the Letter Doubling Map
Steven Widmer (University of North Texas)
TL;DR
This paper explores the combinatorial complexity of infinite permutations derived from binary words under the letter doubling map, providing bounds and explicit formulas for specific classes like Sturmian and Thue-Morse words.
Contribution
It introduces bounds and exact formulas for the permutation complexity of infinite words transformed by the letter doubling map, focusing on Sturmian and Thue-Morse sequences.
Findings
Upper bound for permutation complexity of general words
Exact complexity formulas for Sturmian words
Complexity analysis for Thue-Morse word
Abstract
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated with the image of uniformly recurrent aperiodic binary words under the letter doubling map. An upper bound for the complexity is found for general words, and a formula for the complexity is established for the Sturmian words and the Thue-Morse word.
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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Chemical Synthesis and Analysis