31 citations · 85 across the 14 of their papers we have counts for
14 papers
On the 2-binomial complexity of the generalized Thue-Morse words
Xiao-Tao Lü, Jin Chen, Zhi-Xiong Wen +1
In this paper, we study the -binomial complexity of the generalized Thue-Morse words for every integer . We obtain the exact…
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…
On the abelian complexity of generalized Thue-Morse sequences
Jin Chen, Zhi-Xiong Wen
In this paper, we study the abelian complexity of generalized Thue-Morse sequences . We obtain the exact value of $ρ_n^{ab}(\mathbf{t…
On the additive complexity of a Thue-Morse like sequence
Jin Chen, Zhixiong Wen, Wen Wu
In this paper, we study the additive complexity of a Thue-Morse like sequence with the morphism . W…
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 abelian complexity of the Rudin-Shapiro sequence
Xiaotao Lü, Jin Chen, Zhixiong Wen +1
In this paper, we study the abelian complexity of the Rudin-Shapiro sequence and a related sequence. We show that these two sequences share the same complexity function whic…
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.…
Complexity of Substitutive Sequences - Calculation of the Complexities of Substitutive Sequences Over a Binary Alphabet
Bo Tan, Zhi-Xiong Wen, Yiping Zhang
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity…
Remarks on dimensions of Cartesian product sets
Chun Wei, Shengyou Wen, Zhixiong Wen
Given metric spaces and , it is well known that an…
Hankel determinants of the Cantor sequence
Zhi-xiong Wen, Wen Wu
In the paper, we give the recurrent equations of the Hankel determinants of the Cantor sequence, and show that the Hankel determinants as a double sequence is 3-automatic. With the…
Doubling measures on uniform Cantor sets
Chun Wei, Shengyou Wen, Zhixiong Wen
We obtain a complete description for a probability measure to be doubling on an arbitrarily given uniform Cantor set. The question of which doubling measures on such a Cantor set c…
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…
On the irrationality exponent of the regular paperfolding numbers
Yingjun Guo, Wen Wu, Zhixiong Wen
In this paper, improving the method of Allouche \emph{et al.} \cite{APWW98}, we calculate the Hankel determinant of the regular paperfolding sequence, and prove that the Hankel det…