English

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 π\pi of X is a linear ordering <π<_\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.

Keywords

Cite

@article{arxiv.1102.5527,
  title  = {Permutation Complexity and the Letter Doubling Map},
  author = {Steven Widmer},
  journal= {arXiv preprint arXiv:1102.5527},
  year   = {2011}
}
R2 v1 2026-06-21T17:32:37.508Z