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arXiv · 1102.5527

Permutation Complexity and the Letter Doubling Map

Steven Widmer
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Abstract

Given a countable set X (usually taken to be N or Z), an infinite permutation $π$ of X is a linear ordering $<_π$ of X. This paper investigates the combinatorial complexity of infinite permutations on N 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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Steven Widmer. 2011-02-27. Permutation Complexity and the Letter Doubling Map. https://arxiv.org/abs/1102.5527

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