Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences
Allouche, Jean-Paul · Shallit, Jeffrey · Wen, Zhixiong · Wu, Wen · Zhang, Jiemeng
Original · EN
First, we show that the sum-free set generated by the period-doubling sequence is not κ-regular for any κ≥ 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 κ-regular for all κ≥ 2. Finally, we study the sum-free sets generated by Sturmian sequences that begin with `11', and their difference sequences.
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