Permutation Complexity Related to the Letter Doubling Map

Details Permutation Complexity Related to the Letter Doubling Map Permutation Complexity Related to the Letter Doubling Map

2011-08-18

arxiv.org/abs/1108.3642v1

EPTCS 63, 2011, pp. 265-276

Computer Science

Discrete Mathematics

In Proceedings WORDS 2011, arXiv:1108.3412

Scientific paper

10.4204/EPTCS.63.33

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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