Permutation Complexity and the Letter Doubling Map

Details Permutation Complexity and the Letter Doubling Map Permutation Complexity and the Letter Doubling Map

2011-02-27

arxiv.org/abs/1102.5527v1

Mathematics

Combinatorics

Scientific paper

Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ 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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