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Mosc. Math. J., 2018, Volume 18, Number 2, Pages 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

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.

Full text: http://www.mathjournals.org/.../2018-018-002-003.html
References: PDF file   HTML file

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
\Bibitem{Dev18}
\by Rostislav Devyatov
\paper On factor complexity of morphic sequences
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 2
\pages 211--303
\mathnet{http://mi.mathnet.ru/mmj672}


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