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

摘要

First, we show that the sum-free set generated by the period-doubling sequence is not kappa-regular for any is kappa >= 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 is kappa >= 2. Finally, we study the sum-free sets generated by Sturmian sequences that begin with '11', and their difference sequences.

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