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Moscow Mathematical Journal

Volume 18, Issue 2, April–June 2018  pp. 211–303.

On Factor Complexity of Morphic Sequences

Authors:  Rostislav Devyatov (1)
Author institution:(1) Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward, Ottawa, ON, K1N 6N5, Canada


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 Θ(n1+1/k) for some k∈ℕ, or is O(n log n).

2010 Math. Subj. Class. Primary: 68R15, 05A05; Secondary: 20M05.

Keywords: Morphic sequence, pure morphic sequence, factor complexity

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