Continued fraction algorithm for Sturmian colorings of trees

被引：0
|
作者：
Kim, Dong Han [1 ]
Lim, Seonhee [2 ]
机构：
[1] Dongguk Univ Seoul, Dept Math Educ, 30 Pildong Ro 1 Gil, Seoul 04620, South Korea
[2] Seoul Natl Univ, Dept Math Sci, Kwanak Ro 1, Seoul 08826, South Korea
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2019年 / 39卷
基金：
新加坡国家研究基金会;
关键词：
COMPLEXITY;
D O I：
10.1017/etds.2017.127
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Factor complexity b(n) (phi) for a vertex coloring phi of a regular tree is the number of classes of n-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity b(n) (phi) = n + 2. In this article, we prove an induction algorithm for Sturmian colorings using colored balls in a way analogous to the continued fraction algorithm for Sturmian words. Furthermore, we characterize Sturmian colorings in terms of the data appearing in the induction algorithm.
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页码：2541 / 2569
页数：29
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