类康托序列的k-Abelian复杂度  

On the k-Abelian Complexity of the Cantor-like Sequence

作　　者：吕小涛 LV Xiaotao(College of Science,Huazhong Agricultural University,Wuhan 430070,China)

机构地区：[1]华中农业大学理学院,湖北武汉430070

出　　处：《应用数学》2023年第4期1100-1108,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11801203)。

摘　　要：本文研究类康托序列c的k-abelian复杂度问题,其中序列c为代换σ:1→10^(l)1,0→0^(l+2)的以1开始的不动点.对任意的k=l,…,l,我们证明若u,v是c的两个因子且它们的长为k的前后缀分别相同,则u,v是(k+1)-abelian等价当且仅当u,v是k-abelian等价的.进一步,我们证明类康托序列c的abelian复杂度和2-abelian复杂度均为(l+2)-正则的.In this paper,we study the k-abelian complexity P(k)c(n)of the Cantor-like sequence c,which is defined as the fixed point of the morphismσ:17→10^(l) 1,07→0^(l+2) beginning with 1 for every integer l≥2.We show that for every integer k with 1≤k≤l,two factors u and v of the Cantor-like sequence which share the same prefix and suffix of length k are(k+1)-abelian equivalent if and only if they are k-abelian equivalent.Moreover,we show that the abelian complexity function and 2-abelian complexity function of the Cantor-like sequence are both(l+2)-regular.

关 键 词：类康托序列 k-abelian等价 k-abelian复杂度 b-正则序列 

分 类 号：O157[理学—数学]