Abstract
Given a countable set X (usually taken to be N or Z ), an infinite permutation π of X is a linear ordering ≺ π of X, introduced in Fon-Der-Flaass and Frid (2007) [5]. This paper investigates the combinatorial complexity of the infinite permutation on N associated with the well-known and well-studied Thue–Morse word. A formula for the complexity is established by studying patterns in subpermutations and the action of the Thue–Morse morphism on the subpermutations.
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