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Moscow Mathematical Journal, 2018, Volume 18, Number 2, Pages 211–303
DOI: https://doi.org/10.17323/1609-4514-2018-18-2-211-303 (Mi mmj672) 		 
On factor complexity of morphic sequences

Rostislav Devyatov

Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward, Ottawa, ON, K1N 6N5, Canada
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DOI: https://doi.org/10.17323/1609-4514-2018-18-2-211-303
Abstract: The paper is devoted to an object well known in combinatorics of words, namely to so-called morphic sequences. The main goal of the paper is to solve (at least partially) the following question raised by J.-J. Pansiot in 1985: what can the factor complexity function of an arbitrary morphic sequence be?
We study structure of pure morphic and morphic sequences and prove the following result: the factor complexity of an arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n\log n)$.
Key words and phrases: morphic sequence, pure morphic sequence, factor complexity.
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Document Type: Article
MSC: Primary 68R15, 05A05; Secondary 20M05
Language: English
Citation: Rostislav Devyatov, “On factor complexity of morphic sequences”, Mosc. Math. J., 18:2 (2018), 211–303
Citation in format AMSBIB
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