7 citations · 8 across the 5 of their papers we have counts for
5 papers
Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences
Jean-Paul Allouche, Jeffrey Shallit, Zhixiong Wen +2
First, we show that the sum-free set generated by the period-doubling sequence is not -regular for any . Next, we introduce a generalization of the period-doubling sequ…
Morphisms on infinite alphabets, countable states automata and regular sequences
Jie-Meng Zhang, Jin Chen, Yingjun Guo +1
In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by co…
On the rational approximations to the real numbers corresponding to the differences of the Fibonacci sequence
Ying-jun Guo, Zhi-xiong Wen, Jie-meng Zhang
Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents…
On the regularity of
Jiemeng Zhang, Yingjun Guo, Zhixiong Wen
Let be real numbers and be an integer. Allouche and Shallit showed that the sequence is -regular if and only if is rational.…
On the regular sum-free sets
Zhi-Xiong Wen, Wen Wu, Jie-Meng Zhang
Cameron introduced a bijection between the set of sum-free sets and the set of all zero-one sequences. In this paper, we study the sum-free sets of natural numbers corresponding to…