Permutation Complexity of the Thue-Morse Word

Details Permutation Complexity of the Thue-Morse Word Permutation Complexity of the Thue-Morse Word

2010-03-31

arxiv.org/abs/1003.6123v2

Mathematics

Combinatorics

Scientific paper

Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers 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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