Permutation Complexity Related to the Letter Doubling Map

Steven Widmer
(University of North Texas)

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

In Petr Ambrož, Štěpán Holub and Zuzana Masáková: Proceedings 8th International Conference Words 2011 (WORDS 2011), Prague, Czech Republic, 12-16th September 2011, Electronic Proceedings in Theoretical Computer Science 63, pp. 265–276.
Published: 17th August 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.63.33 bibtex PDF
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