
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 socalled 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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http://www.mathjournals.org/.../2018018002003.html
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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
\Bibitem{Dev18}
\by Rostislav Devyatov
\paper On factor complexity of morphic sequences
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 2
\pages 211303
\mathnet{http://mi.mathnet.ru/mmj672}
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http://mi.mathnet.ru/eng/mmj672 http://mi.mathnet.ru/eng/mmj/v18/i2/p211
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