ON THE EXPANSIONS OF REAL NUMBERS IN TWO INTEGER BASES

被引：0

作者：

Bugeaud, Yann ^{[1
]}

Kim, Dong Han ^{[2
]}

机构：

[1] Univ Strasbourg, CNRS, UMR 7501, IRMA, 7 Rue Rene Descartes, F-67084 Strasbourg, France

[2] Dongguk Univ Seoul, Dept Math Educ, 30 Pildong Ro,1 Gil, Seoul 04620, South Korea

来源：

ANNALES DE L INSTITUT FOURIER | 2017年 / 67卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Combinatorics on words; Sturmian word; complexity; integer base expansion; continued fraction;

D O I：

10.5802/aif.3134

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let r and s be multiplicatively independent positive integers. We establish that the r-ary expansion and the s-ary expansion of an irrational real number, viewed as infinite words on {0, 1...., r - 1} and {0, 1,., s - 1}, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words.

引用

页码：2225 / 2235

页数：11

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