On the infinite permutation generated by the period doubling word

摘要

The paper is devoted to the properties of infinite permutations. We introduce the infinite permutation xi, in some sense similar to the period doubling word w (which is the fixed point of the morphism phi(w):0 bar right arrow 0100, 1 bar right arrow 0101). We investigate combinatorial properties of xi and find the complexity of xi. (C) 2009 Elsevier Ltd. All rights reserved.