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arXiv · 1809.06554

On the abelian complexity of generalized Thue-Morse sequences

Jin Chen·Zhi-Xiong Wen
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Abstract

In this paper, we study the abelian complexity $ρ_n^{ab}(\mathbf{t}^{(k)})$ of generalized Thue-Morse sequences $\mathbf{t}^{(k)}$. We obtain the exact value of $ρ_n^{ab}(\mathbf{t}^{(k)})$ for every integer $n\geq k$. Consequently, $ρ_n^{ab}(\mathbf{t}^{(k)})$ is ultimately periodic with the period $k$. Moreover, we show that the abelian complexities of a class of infinite sequences are $k$-automatic.

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Jin Chen, Zhi-Xiong Wen. 2019-04-10. On the abelian complexity of generalized Thue-Morse sequences. https://doi.org/10.1016/j.tcs.2019.02.014

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