Permutation Complexity and the Letter Doubling Map
Combinatorics
2011-03-01 v1
Abstract
Given a countable set X (usually taken to be N or Z), an infinite permutation of X is a linear ordering 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.
Cite
@article{arxiv.1102.5527,
title = {Permutation Complexity and the Letter Doubling Map},
author = {Steven Widmer},
journal= {arXiv preprint arXiv:1102.5527},
year = {2011}
}