Permutation Complexity Related to the Letter Doubling Map
Discrete Mathematics
2011-08-19 v1
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.
Cite
@article{arxiv.1108.3642,
title = {Permutation Complexity Related to the Letter Doubling Map},
author = {Steven Widmer},
journal= {arXiv preprint arXiv:1108.3642},
year = {2011}
}
Comments
In Proceedings WORDS 2011, arXiv:1108.3412