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arXiv · 1911.01687

Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences

Jean-Paul Allouche·Jeffrey Shallit·Zhixiong Wen·Wen Wu·Jiemeng Zhang
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Abstract

First, we show that the sum-free set generated by the period-doubling sequence is not $\kappa$-regular for any $\kappa\geq 2$. Next, we introduce a generalization of the period-doubling sequence, which we call the period-$k$-folding sequences. We show that the sum-free sets generated by the period-$k$-folding sequences also fail to be $\kappa$-regular for all $\kappa\geq 2$. Finally, we study the sum-free sets generated by Sturmian sequences that begin with `11', and their difference sequences.

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Jean-Paul Allouche, Jeffrey Shallit, Zhixiong Wen, Wen Wu, Jiemeng Zhang. 2019-11-05. Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences. https://arxiv.org/abs/1911.01687

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