On an infinite permutation similar to the Thue-Morse word

@article{Makarov2009OnAI,
  title={On an infinite permutation similar to the Thue-Morse word},
  author={M. A. Makarov},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={6641-6643}
}
Infinite permutations (in our sense) were introduced in 2005 by Fon-Der-Flaass and Frid. We introduce an infinite permutation τ in some sense similar to the Thue–Morse word w (where w is the fixed point of the morphism φw: 0 7→ 01, 1 7→ 10). We suggest two essentially different definitions of τ and show their equivalence. © 2009 Elsevier B.V. All rights reserved.